Topic: Trigonometric Functions |
Common Core Mathematics 9-12 |
| Cluster Extend the domain of trigonometric functions using the unit circle |
| | Grade 9-12 |
| | | F.TF.1. | Understand radian measure of an angle as the length of the arc on the
unit circle subtended by the angle. |
| | | F.TF.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. |
| | | F.TF.3. | (+) Use special triangles to determine geometrically the values of sine,
cosine, tangent for ∏/3, ∏/4 and ∏/6, and use the unit circle to express
the values of sine, cosine, and tangent for ∏–x, ∏+x, and 2 ∏ –x in terms
of their values for x, where x is any real number. |
| | | F.TF.4. | (+) Use the unit circle to explain symmetry (odd and even) and
periodicity of trigonometric functions. |
| Cluster Model periodic phenomena with trigonometric functions |
| | Grade 9-12 |
| | | F.TF.5. | Choose trigonometric functions to model periodic phenomena with
specified amplitude, frequency, and midline. |
| | | F.TF.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. |
| | | F.TF.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. |
| Cluster Prove and apply trigonometric identities |
| | Grade 9-12 |
| | | F.TF.8. | Prove the Pythagorean identity sin^{2}(θ) + cos^{2}(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. |
| | | F.TF.9. | (+) Prove the addition and subtraction formulas for sine, cosine, and
tangent and use them to solve problems. |