Use special triangles and unit circle

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HSF.TF.A.3

**HSF.TF.A.3**: (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4 and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for pi-x, pi+x, and 2pi-x in terms of their values for x, where x is the measure of an angle.

HSF.TF.A.3: (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4 and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for pi-x, pi+x, and 2pi-x in terms of their values for x, where x is the measure of an angle.

What you'll learn

Derive the side ratios of a 45-45-90 triangle (1 : 1 : sqrt(2)) and a 30-60-90 triangle (1 : sqrt(3) : 2) from geometric reasoning
Use the 45-45-90 triangle to find exact values of sin, cos, and tan at pi/4
Use the 30-60-90 triangle to find exact values of sin, cos, and tan at pi/6 and pi/3
Place these special triangles in the unit circle to determine coordinates at pi/6, pi/4, and pi/3
Use unit circle symmetry to express sin, cos, and tan of pi - x, pi + x, and 2pi - x in terms of their values at x
Apply reference angle relationships to evaluate trig functions at any multiple of pi/6 or pi/4

Review first:

Extend trigonometric functions using unit circle

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Special triangles exact values

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