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Основно съдържание

STANDARDS

Math

Common Core Math

High School: Functions: Trigonometric Functions

HSF.TF.A

Extend the domain of trigonometric functions using the unit circle.

HSF.TF.A.1

Not covered
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
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HSF.TF.A.2

Not covered
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.
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HSF.TF.A.3

Mostly covered
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, cosine, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is any real number.

HSF.TF.A.4

Fully covered
Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

HSF.TF.B

Model periodic phenomena with trigonometric functions.

HSF.TF.B.5

Fully covered
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

HSF.TF.B.6

Mostly covered
Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

HSF.TF.B.7

Mostly covered
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.

HSF.TF.C

Prove and apply trigonometric identities.

HSF.TF.C.8

Fully covered
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.

HSF.TF.C.9

Fully covered
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.