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**Standard(s): **
[MA2015] GEO (9-12) 27 :

[MA2015] PRE (9-12) 29 :

[MA2015] PRE (9-12) 30 :

[MA2015] PRE (9-12) 34 :

27 ) (+) Construct a tangent line from a point outside a given circle to the circle. [G-C4]

[MA2015] PRE (9-12) 29 :

29 ) (+) Use special triangles to determine geometrically the values of sine, cosine, and 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. [F-TF3]

[MA2015] PRE (9-12) 30 :

30 ) (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. [F-TF4]

[MA2015] PRE (9-12) 34 :

34 ) (+) Prove the addition and subtraction formulas for sine, cosine, and tangent, and use them to solve problems. [F-TF9]

Module 4, Topic A helps students recall how to use special triangles positioned within the unit circle to determine geometrically the values of sine, cosine, and tangent at special angles. The unit circle is used to study the values of sine, cosine, and tangent and to explain the periodicity of the trigonometric functions and their symmetries. Students develop the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems and to model geometric phenomena. Students model waves, waves traveling together, and wave patterns generated by musical instruments.

**Note: This module is identified as Precalculus and Advanced Topics in the EngageNY curriculum. It also corresponds to the Geometry Course of Study.**