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Everything you need to get ready for calculus

## (1) Getting started

- Welcome to Trigonometry!
- Complementary and supplementary angles
- Sketching angles in standard position
- Quadrant of the angle
- Converting between degrees and dms
- Finding coterminal angles
- Finding coterminal angles, example 2
- Converting between degrees and radians
- Converting between degrees and radians, example 2
- Oriented arc for a real number
- Area of a circular sector
- Finding sine and cosine of an angle theta
- Finding sine given cosine, or vice versa
- All possible values for the angle theta
- All possible values for the angle theta, example 2
- All possible values for the real number t
- Completing a triangle
- Finding the side lengths of the triangle
- Given a point on the terminal side of the angle
- Find the value or say where the function is undefined
- Find all six trig functions given the quadrant of the angle
- Find all six trig functions at the coordinate point
- Find all six trig functions using reciprocal identities
- Angle of elevation
- Proving the trig equation
- Proving the trig equation with pythagorean identities
- Using even-odd identities
- Using sum-difference identities
- Using sum-difference identities, example 2
- Using sum-difference identities, example 3
- Using half-angle identities
- Using double-angle identities to prove the equation
- Using product-to-sum identities
- Using sum-to-product identities
- Using trig identities to prove the equation
- List the solutions of the equation inside the interval
- List the solutions of the equation inside the interval, example 2
- Finding the value of an inverse trig function
- Period and amplitude
- Sketching sine and cosine
- Comparing sine and cosine graphs
- Sequence of transformations
- Law of sines
- Law of sines for area of a triangle
- Law of cosines
- Heron's formula for area of a triangle
- Converting polar coordinates to rectangular
- Converting rectangular coordinates to polar
- Express the polar point multiple ways
- Converting equations from polar to rectangular
- Converting equations from rectangular to polar
- Graph the polar curve, circle
- Graph the polar curve, rose
- Graph the polar curve, cardioid
- Graph the polar curve, limacon
- Graph the polar curve, lemniscate
- Intersection points of the polar curves
- Graph the polar region in the xy-plane
- Sketching a parametric curve and its orientation
- Write the equation as a parametric curve

## (2) Introduction to angles

- Welcome to Trigonometry!
- Complementary and supplementary angles
- Sketching angles in standard position
- Quadrant of the angle
- Converting between degrees and dms
- Finding coterminal angles
- Finding coterminal angles, example 2
- Converting between degrees and radians
- Converting between degrees and radians, example 2
- Oriented arc for a real number
- Area of a circular sector
- Finding sine and cosine of an angle theta
- Finding sine given cosine, or vice versa
- All possible values for the angle theta
- All possible values for the angle theta, example 2
- All possible values for the real number t
- Completing a triangle
- Finding the side lengths of the triangle
- Given a point on the terminal side of the angle
- Find the value or say where the function is undefined
- Find all six trig functions given the quadrant of the angle
- Find all six trig functions at the coordinate point
- Find all six trig functions using reciprocal identities
- Angle of elevation
- Proving the trig equation
- Proving the trig equation with pythagorean identities
- Using even-odd identities
- Using sum-difference identities
- Using sum-difference identities, example 2
- Using sum-difference identities, example 3
- Using half-angle identities
- Using double-angle identities to prove the equation
- Using product-to-sum identities
- Using sum-to-product identities
- Using trig identities to prove the equation
- List the solutions of the equation inside the interval
- List the solutions of the equation inside the interval, example 2
- Finding the value of an inverse trig function
- Period and amplitude
- Sketching sine and cosine
- Comparing sine and cosine graphs
- Sequence of transformations
- Law of sines
- Law of sines for area of a triangle
- Law of cosines
- Heron's formula for area of a triangle
- Converting polar coordinates to rectangular
- Converting rectangular coordinates to polar
- Express the polar point multiple ways
- Converting equations from polar to rectangular
- Converting equations from rectangular to polar
- Graph the polar curve, circle
- Graph the polar curve, rose
- Graph the polar curve, cardioid
- Graph the polar curve, limacon
- Graph the polar curve, lemniscate
- Intersection points of the polar curves
- Graph the polar region in the xy-plane
- Sketching a parametric curve and its orientation
- Write the equation as a parametric curve

## (3) Angles and their measure

- Welcome to Trigonometry!
- Complementary and supplementary angles
- Sketching angles in standard position
- Quadrant of the angle
- Converting between degrees and dms
- Finding coterminal angles
- Finding coterminal angles, example 2
- Converting between degrees and radians
- Converting between degrees and radians, example 2
- Oriented arc for a real number
- Area of a circular sector
- Finding sine and cosine of an angle theta
- Finding sine given cosine, or vice versa
- All possible values for the angle theta
- All possible values for the angle theta, example 2
- All possible values for the real number t
- Completing a triangle
- Finding the side lengths of the triangle
- Given a point on the terminal side of the angle
- Find the value or say where the function is undefined
- Find all six trig functions given the quadrant of the angle
- Find all six trig functions at the coordinate point
- Find all six trig functions using reciprocal identities
- Angle of elevation
- Proving the trig equation
- Proving the trig equation with pythagorean identities
- Using even-odd identities
- Using sum-difference identities
- Using sum-difference identities, example 2
- Using sum-difference identities, example 3
- Using half-angle identities
- Using double-angle identities to prove the equation
- Using product-to-sum identities
- Using sum-to-product identities
- Using trig identities to prove the equation
- List the solutions of the equation inside the interval
- List the solutions of the equation inside the interval, example 2
- Finding the value of an inverse trig function
- Period and amplitude
- Sketching sine and cosine
- Comparing sine and cosine graphs
- Sequence of transformations
- Law of sines
- Law of sines for area of a triangle
- Law of cosines
- Heron's formula for area of a triangle
- Converting polar coordinates to rectangular
- Converting rectangular coordinates to polar
- Express the polar point multiple ways
- Converting equations from polar to rectangular
- Converting equations from rectangular to polar
- Graph the polar curve, circle
- Graph the polar curve, rose
- Graph the polar curve, cardioid
- Graph the polar curve, limacon
- Graph the polar curve, lemniscate
- Intersection points of the polar curves
- Graph the polar region in the xy-plane
- Sketching a parametric curve and its orientation
- Write the equation as a parametric curve

## (4) The unit circle

- Welcome to Trigonometry!
- Complementary and supplementary angles
- Sketching angles in standard position
- Quadrant of the angle
- Converting between degrees and dms
- Finding coterminal angles
- Finding coterminal angles, example 2
- Converting between degrees and radians
- Converting between degrees and radians, example 2
- Oriented arc for a real number
- Area of a circular sector
- Finding sine and cosine of an angle theta
- Finding sine given cosine, or vice versa
- All possible values for the angle theta
- All possible values for the angle theta, example 2
- All possible values for the real number t
- Completing a triangle
- Finding the side lengths of the triangle
- Given a point on the terminal side of the angle
- Find the value or say where the function is undefined
- Find all six trig functions given the quadrant of the angle
- Find all six trig functions at the coordinate point
- Find all six trig functions using reciprocal identities
- Angle of elevation
- Proving the trig equation
- Proving the trig equation with pythagorean identities
- Using even-odd identities
- Using sum-difference identities
- Using sum-difference identities, example 2
- Using sum-difference identities, example 3
- Using half-angle identities
- Using double-angle identities to prove the equation
- Using product-to-sum identities
- Using sum-to-product identities
- Using trig identities to prove the equation
- List the solutions of the equation inside the interval
- List the solutions of the equation inside the interval, example 2
- Finding the value of an inverse trig function
- Period and amplitude
- Sketching sine and cosine
- Comparing sine and cosine graphs
- Sequence of transformations
- Law of sines
- Law of sines for area of a triangle
- Law of cosines
- Heron's formula for area of a triangle
- Converting polar coordinates to rectangular
- Converting rectangular coordinates to polar
- Express the polar point multiple ways
- Converting equations from polar to rectangular
- Converting equations from rectangular to polar
- Graph the polar curve, circle
- Graph the polar curve, rose
- Graph the polar curve, cardioid
- Graph the polar curve, limacon
- Graph the polar curve, lemniscate
- Intersection points of the polar curves
- Graph the polar region in the xy-plane
- Sketching a parametric curve and its orientation
- Write the equation as a parametric curve

## (5) Six circular functions

- Welcome to Trigonometry!
- Complementary and supplementary angles
- Sketching angles in standard position
- Quadrant of the angle
- Converting between degrees and dms
- Finding coterminal angles
- Finding coterminal angles, example 2
- Converting between degrees and radians
- Converting between degrees and radians, example 2
- Oriented arc for a real number
- Area of a circular sector
- Finding sine and cosine of an angle theta
- Finding sine given cosine, or vice versa
- All possible values for the angle theta
- All possible values for the angle theta, example 2
- All possible values for the real number t
- Completing a triangle
- Finding the side lengths of the triangle
- Given a point on the terminal side of the angle
- Find the value or say where the function is undefined
- Find all six trig functions given the quadrant of the angle
- Find all six trig functions at the coordinate point
- Find all six trig functions using reciprocal identities
- Angle of elevation
- Proving the trig equation
- Proving the trig equation with pythagorean identities
- Using even-odd identities
- Using sum-difference identities
- Using sum-difference identities, example 2
- Using sum-difference identities, example 3
- Using half-angle identities
- Using double-angle identities to prove the equation
- Using product-to-sum identities
- Using sum-to-product identities
- Using trig identities to prove the equation
- List the solutions of the equation inside the interval
- List the solutions of the equation inside the interval, example 2
- Finding the value of an inverse trig function
- Period and amplitude
- Sketching sine and cosine
- Comparing sine and cosine graphs
- Sequence of transformations
- Law of sines
- Law of sines for area of a triangle
- Law of cosines
- Heron's formula for area of a triangle
- Converting polar coordinates to rectangular
- Converting rectangular coordinates to polar
- Express the polar point multiple ways
- Converting equations from polar to rectangular
- Converting equations from rectangular to polar
- Graph the polar curve, circle
- Graph the polar curve, rose
- Graph the polar curve, cardioid
- Graph the polar curve, limacon
- Graph the polar curve, lemniscate
- Intersection points of the polar curves
- Graph the polar region in the xy-plane
- Sketching a parametric curve and its orientation
- Write the equation as a parametric curve

## (6) Trig identities

- Welcome to Trigonometry!
- Complementary and supplementary angles
- Sketching angles in standard position
- Quadrant of the angle
- Converting between degrees and dms
- Finding coterminal angles
- Finding coterminal angles, example 2
- Converting between degrees and radians
- Converting between degrees and radians, example 2
- Oriented arc for a real number
- Area of a circular sector
- Finding sine and cosine of an angle theta
- Finding sine given cosine, or vice versa
- All possible values for the angle theta
- All possible values for the angle theta, example 2
- All possible values for the real number t
- Completing a triangle
- Finding the side lengths of the triangle
- Given a point on the terminal side of the angle
- Find the value or say where the function is undefined
- Find all six trig functions given the quadrant of the angle
- Find all six trig functions at the coordinate point
- Find all six trig functions using reciprocal identities
- Angle of elevation
- Proving the trig equation
- Proving the trig equation with pythagorean identities
- Using even-odd identities
- Using sum-difference identities
- Using sum-difference identities, example 2
- Using sum-difference identities, example 3
- Using half-angle identities
- Using double-angle identities to prove the equation
- Using product-to-sum identities
- Using sum-to-product identities
- Using trig identities to prove the equation
- List the solutions of the equation inside the interval
- List the solutions of the equation inside the interval, example 2
- Finding the value of an inverse trig function
- Period and amplitude
- Sketching sine and cosine
- Comparing sine and cosine graphs
- Sequence of transformations
- Law of sines
- Law of sines for area of a triangle
- Law of cosines
- Heron's formula for area of a triangle
- Converting polar coordinates to rectangular
- Converting rectangular coordinates to polar
- Express the polar point multiple ways
- Converting equations from polar to rectangular
- Converting equations from rectangular to polar
- Graph the polar curve, circle
- Graph the polar curve, rose
- Graph the polar curve, cardioid
- Graph the polar curve, limacon
- Graph the polar curve, lemniscate
- Intersection points of the polar curves
- Graph the polar region in the xy-plane
- Sketching a parametric curve and its orientation
- Write the equation as a parametric curve

## (7) Graphing the trig functions

- Welcome to Trigonometry!
- Complementary and supplementary angles
- Sketching angles in standard position
- Quadrant of the angle
- Converting between degrees and dms
- Finding coterminal angles
- Finding coterminal angles, example 2
- Converting between degrees and radians
- Converting between degrees and radians, example 2
- Oriented arc for a real number
- Area of a circular sector
- Finding sine and cosine of an angle theta
- Finding sine given cosine, or vice versa
- All possible values for the angle theta
- All possible values for the angle theta, example 2
- All possible values for the real number t
- Completing a triangle
- Finding the side lengths of the triangle
- Given a point on the terminal side of the angle
- Find the value or say where the function is undefined
- Find all six trig functions given the quadrant of the angle
- Find all six trig functions at the coordinate point
- Find all six trig functions using reciprocal identities
- Angle of elevation
- Proving the trig equation
- Proving the trig equation with pythagorean identities
- Using even-odd identities
- Using sum-difference identities
- Using sum-difference identities, example 2
- Using sum-difference identities, example 3
- Using half-angle identities
- Using double-angle identities to prove the equation
- Using product-to-sum identities
- Using sum-to-product identities
- Using trig identities to prove the equation
- List the solutions of the equation inside the interval
- List the solutions of the equation inside the interval, example 2
- Finding the value of an inverse trig function
- Period and amplitude
- Sketching sine and cosine
- Comparing sine and cosine graphs
- Sequence of transformations
- Law of sines
- Law of sines for area of a triangle
- Law of cosines
- Heron's formula for area of a triangle
- Converting polar coordinates to rectangular
- Converting rectangular coordinates to polar
- Express the polar point multiple ways
- Converting equations from polar to rectangular
- Converting equations from rectangular to polar
- Graph the polar curve, circle
- Graph the polar curve, rose
- Graph the polar curve, cardioid
- Graph the polar curve, limacon
- Graph the polar curve, lemniscate
- Intersection points of the polar curves
- Graph the polar region in the xy-plane
- Sketching a parametric curve and its orientation
- Write the equation as a parametric curve

## (8) The law of sines

- Welcome to Trigonometry!
- Complementary and supplementary angles
- Sketching angles in standard position
- Quadrant of the angle
- Converting between degrees and dms
- Finding coterminal angles
- Finding coterminal angles, example 2
- Converting between degrees and radians
- Converting between degrees and radians, example 2
- Oriented arc for a real number
- Area of a circular sector
- Finding sine and cosine of an angle theta
- Finding sine given cosine, or vice versa
- All possible values for the angle theta
- All possible values for the angle theta, example 2
- All possible values for the real number t
- Completing a triangle
- Finding the side lengths of the triangle
- Given a point on the terminal side of the angle
- Find the value or say where the function is undefined
- Find all six trig functions given the quadrant of the angle
- Find all six trig functions at the coordinate point
- Find all six trig functions using reciprocal identities
- Angle of elevation
- Proving the trig equation
- Proving the trig equation with pythagorean identities
- Using even-odd identities
- Using sum-difference identities
- Using sum-difference identities, example 2
- Using sum-difference identities, example 3
- Using half-angle identities
- Using double-angle identities to prove the equation
- Using product-to-sum identities
- Using sum-to-product identities
- Using trig identities to prove the equation
- List the solutions of the equation inside the interval
- List the solutions of the equation inside the interval, example 2
- Finding the value of an inverse trig function
- Period and amplitude
- Sketching sine and cosine
- Comparing sine and cosine graphs
- Sequence of transformations
- Law of sines
- Law of sines for area of a triangle
- Law of cosines
- Heron's formula for area of a triangle
- Converting polar coordinates to rectangular
- Converting rectangular coordinates to polar
- Express the polar point multiple ways
- Converting equations from polar to rectangular
- Converting equations from rectangular to polar
- Graph the polar curve, circle
- Graph the polar curve, rose
- Graph the polar curve, cardioid
- Graph the polar curve, limacon
- Graph the polar curve, lemniscate
- Intersection points of the polar curves
- Graph the polar region in the xy-plane
- Sketching a parametric curve and its orientation
- Write the equation as a parametric curve

## (9) The law of cosines

- Welcome to Trigonometry!
- Complementary and supplementary angles
- Sketching angles in standard position
- Quadrant of the angle
- Converting between degrees and dms
- Finding coterminal angles
- Finding coterminal angles, example 2
- Converting between degrees and radians
- Converting between degrees and radians, example 2
- Oriented arc for a real number
- Area of a circular sector
- Finding sine and cosine of an angle theta
- Finding sine given cosine, or vice versa
- All possible values for the angle theta
- All possible values for the angle theta, example 2
- All possible values for the real number t
- Completing a triangle
- Finding the side lengths of the triangle
- Given a point on the terminal side of the angle
- Find the value or say where the function is undefined
- Find all six trig functions given the quadrant of the angle
- Find all six trig functions at the coordinate point
- Find all six trig functions using reciprocal identities
- Angle of elevation
- Proving the trig equation
- Proving the trig equation with pythagorean identities
- Using even-odd identities
- Using sum-difference identities
- Using sum-difference identities, example 2
- Using sum-difference identities, example 3
- Using half-angle identities
- Using double-angle identities to prove the equation
- Using product-to-sum identities
- Using sum-to-product identities
- Using trig identities to prove the equation
- List the solutions of the equation inside the interval
- List the solutions of the equation inside the interval, example 2
- Finding the value of an inverse trig function
- Period and amplitude
- Sketching sine and cosine
- Comparing sine and cosine graphs
- Sequence of transformations
- Law of sines
- Law of sines for area of a triangle
- Law of cosines
- Heron's formula for area of a triangle
- Converting polar coordinates to rectangular
- Converting rectangular coordinates to polar
- Express the polar point multiple ways
- Converting equations from polar to rectangular
- Converting equations from rectangular to polar
- Graph the polar curve, circle
- Graph the polar curve, rose
- Graph the polar curve, cardioid
- Graph the polar curve, limacon
- Graph the polar curve, lemniscate
- Intersection points of the polar curves
- Graph the polar region in the xy-plane
- Sketching a parametric curve and its orientation
- Write the equation as a parametric curve

## (10) Polar coordinates

- Welcome to Trigonometry!
- Complementary and supplementary angles
- Sketching angles in standard position
- Quadrant of the angle
- Converting between degrees and dms
- Finding coterminal angles
- Finding coterminal angles, example 2
- Converting between degrees and radians
- Converting between degrees and radians, example 2
- Oriented arc for a real number
- Area of a circular sector
- Finding sine and cosine of an angle theta
- Finding sine given cosine, or vice versa
- All possible values for the angle theta
- All possible values for the angle theta, example 2
- All possible values for the real number t
- Completing a triangle
- Finding the side lengths of the triangle
- Given a point on the terminal side of the angle
- Find the value or say where the function is undefined
- Find all six trig functions given the quadrant of the angle
- Find all six trig functions at the coordinate point
- Find all six trig functions using reciprocal identities
- Angle of elevation
- Proving the trig equation
- Proving the trig equation with pythagorean identities
- Using even-odd identities
- Using sum-difference identities
- Using sum-difference identities, example 2
- Using sum-difference identities, example 3
- Using half-angle identities
- Using double-angle identities to prove the equation
- Using product-to-sum identities
- Using sum-to-product identities
- Using trig identities to prove the equation
- List the solutions of the equation inside the interval
- List the solutions of the equation inside the interval, example 2
- Finding the value of an inverse trig function
- Period and amplitude
- Sketching sine and cosine
- Comparing sine and cosine graphs
- Sequence of transformations
- Law of sines
- Law of sines for area of a triangle
- Law of cosines
- Heron's formula for area of a triangle
- Converting polar coordinates to rectangular
- Converting rectangular coordinates to polar
- Express the polar point multiple ways
- Converting equations from polar to rectangular
- Converting equations from rectangular to polar
- Graph the polar curve, circle
- Graph the polar curve, rose
- Graph the polar curve, cardioid
- Graph the polar curve, limacon
- Graph the polar curve, lemniscate
- Intersection points of the polar curves
- Graph the polar region in the xy-plane
- Sketching a parametric curve and its orientation
- Write the equation as a parametric curve

## (11) Graphing polar curves

- Welcome to Trigonometry!
- Complementary and supplementary angles
- Sketching angles in standard position
- Quadrant of the angle
- Converting between degrees and dms
- Finding coterminal angles
- Finding coterminal angles, example 2
- Converting between degrees and radians
- Converting between degrees and radians, example 2
- Oriented arc for a real number
- Area of a circular sector
- Finding sine and cosine of an angle theta
- Finding sine given cosine, or vice versa
- All possible values for the angle theta
- All possible values for the angle theta, example 2
- All possible values for the real number t
- Completing a triangle
- Finding the side lengths of the triangle
- Given a point on the terminal side of the angle
- Find the value or say where the function is undefined
- Find all six trig functions given the quadrant of the angle
- Find all six trig functions at the coordinate point
- Find all six trig functions using reciprocal identities
- Angle of elevation
- Proving the trig equation
- Proving the trig equation with pythagorean identities
- Using even-odd identities
- Using sum-difference identities
- Using sum-difference identities, example 2
- Using sum-difference identities, example 3
- Using half-angle identities
- Using double-angle identities to prove the equation
- Using product-to-sum identities
- Using sum-to-product identities
- Using trig identities to prove the equation
- List the solutions of the equation inside the interval
- List the solutions of the equation inside the interval, example 2
- Finding the value of an inverse trig function
- Period and amplitude
- Sketching sine and cosine
- Comparing sine and cosine graphs
- Sequence of transformations
- Law of sines
- Law of sines for area of a triangle
- Law of cosines
- Heron's formula for area of a triangle
- Converting polar coordinates to rectangular
- Converting rectangular coordinates to polar
- Express the polar point multiple ways
- Converting equations from polar to rectangular
- Converting equations from rectangular to polar
- Graph the polar curve, circle
- Graph the polar curve, rose
- Graph the polar curve, cardioid
- Graph the polar curve, limacon
- Graph the polar curve, lemniscate
- Intersection points of the polar curves
- Graph the polar region in the xy-plane
- Sketching a parametric curve and its orientation
- Write the equation as a parametric curve

## (12) Parametric curves

- Welcome to Trigonometry!
- Complementary and supplementary angles
- Sketching angles in standard position
- Quadrant of the angle
- Converting between degrees and dms
- Finding coterminal angles
- Finding coterminal angles, example 2
- Converting between degrees and radians
- Converting between degrees and radians, example 2
- Oriented arc for a real number
- Area of a circular sector
- Finding sine and cosine of an angle theta
- Finding sine given cosine, or vice versa
- All possible values for the angle theta
- All possible values for the angle theta, example 2
- All possible values for the real number t
- Completing a triangle
- Finding the side lengths of the triangle
- Given a point on the terminal side of the angle
- Find the value or say where the function is undefined
- Find all six trig functions given the quadrant of the angle
- Find all six trig functions at the coordinate point
- Find all six trig functions using reciprocal identities
- Angle of elevation
- Proving the trig equation
- Proving the trig equation with pythagorean identities
- Using even-odd identities
- Using sum-difference identities
- Using sum-difference identities, example 2
- Using sum-difference identities, example 3
- Using half-angle identities
- Using double-angle identities to prove the equation
- Using product-to-sum identities
- Using sum-to-product identities
- Using trig identities to prove the equation
- List the solutions of the equation inside the interval
- List the solutions of the equation inside the interval, example 2
- Finding the value of an inverse trig function
- Period and amplitude
- Sketching sine and cosine
- Comparing sine and cosine graphs
- Sequence of transformations
- Law of sines
- Law of sines for area of a triangle
- Law of cosines
- Heron's formula for area of a triangle
- Converting polar coordinates to rectangular
- Converting rectangular coordinates to polar
- Express the polar point multiple ways
- Converting equations from polar to rectangular
- Converting equations from rectangular to polar
- Graph the polar curve, circle
- Graph the polar curve, rose
- Graph the polar curve, cardioid
- Graph the polar curve, limacon
- Graph the polar curve, lemniscate
- Intersection points of the polar curves
- Graph the polar region in the xy-plane
- Sketching a parametric curve and its orientation
- Write the equation as a parametric curve

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