Mathematics » High School: Functions » Trigonometric Functions

Extend the domain of trigonometric functions using the unit circle.

• 1. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

  Suggested tag: cc-9-12m-f-tf-1

• 2. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

  Suggested tag: cc-9-12m-f-tf-2

• 3. (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosines, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is any real number.

  Suggested tag: cc-9-12m-f-tf-3

• 4. (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

  Suggested tag: cc-9-12m-f-tf-4

Model periodic phenomena with trigonometric functions.

• 5. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.^★

  Suggested tag: cc-9-12m-f-tf-5

• 6. (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

  Suggested tag: cc-9-12m-f-tf-6

• 7. (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.^★

  Suggested tag: cc-9-12m-f-tf-7

Prove and apply trigonometric identities.

• 8. Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

  Suggested tag: cc-9-12m-f-tf-8

• 9. (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

  Suggested tag: cc-9-12m-f-tf-9