13-5 The Cosine Function

Objectives

To graph and write cosine functions

To solve trigonometric equations

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The cosine function, y = cos θ , y equals cosine theta comma  matches θ with the x-coordinate of the point on the unit circle where the terminal side of angle θ intersects the unit circle. The symmetry of the set of points ( x , y ) = ( cos θ , sin θ ) open x comma y close equals open cosine theta comma sine theta close  on the unit circle guarantees that the graphs of sine and cosine are congruent translations of each other.

Essential Understanding As the terminal side of an angle rotates about the origin (beginning at 0°), its cosine value on the unit circle decreases from 1 to − 1 , negative 1 comma  and then increases back to 1.

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