Consider the trigonometric functions defined on the unit circle.

MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

Consider the trigonometric functions defined on the unit circle. (a) Explain, with the help of the unit-circle definition, why the x-coordinate of a point at an angle xx equals the y-coordinate of a point at an angle π2−x\dfrac{\pi}{2}-x. (b) Hence justify the relation cos⁡x=sin⁡(π2−x)\cos x = \sin\left(\dfrac{\pi}{2}-x\right) for all real xx. (c) Describe how the above relation affects the symmetry of the graphs of y=sin⁡xy=\sin x and y=cos⁡xy=\cos x.

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