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STANDARDS

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US-SC

Math

South Carolina Math

Pre-Calculus: Trigonometry

PC.FT.1

Not covered
Understand that the radian measure of an angle is the length of the arc on the unit circle subtended by the angle.
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PC.FT.2

Define sine and cosine as functions of the radian measure of an angle in terms of the x- and y-coordinates of the point on the unit circle corresponding to that angle and explain how these definitions are extensions of the right triangle definitions.

PC.FT.2a

Partially covered
Define the tangent, cotangent, secant, and cosecant functions as ratios involving sine and cosine.

PC.FT.2b

Partially covered
Write cotangent, secant, and cosecant functions as the reciprocals of tangent, cosine, and sine, respectively.

PC.FT.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 π-x, π+x, and 2π-x in terms of their values for x, where x is any real number.

PC.FT.4

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

PC.FT.5

Fully covered
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
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PC.FT.6

Fully covered
Define the six inverse trigonometric functions using domain restrictions for regions where the function is always increasing or always decreasing.

PC.FT.7

Fully 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.

PC.FT.8

Mostly covered
Justify the Pythagorean, even/odd, and cofunction identities for sine and cosine using their unit circle definitions and symmetries of the unit circle and use the Pythagorean identity to find sin A, cos A, or tan A, given sin A, cos A, or tan A, and the quadrant of the angle.

PC.FT.9

Fully covered
Justify the sum and difference formulas for sine, cosine, and tangent and use them to solve problems.