Answer the following questions related to the symmetry of trigonometric functions:

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

Problem

Answer the following questions related to the symmetry of trigonometric functions: (i) Show that sin⁡(180∘−θ)=sin⁡θ\sin(180^\circ-\theta)=\sin\theta for any real angle θ\theta. (ii) Show that cos⁡(180∘−θ)=−cos⁡θ\cos(180^\circ-\theta)=-\cos\theta for any real angle θ\theta. (iii) Explain, with reference to the signs of the coordinates of a point on the unit circle, why the results obtained in (i) and (ii) agree with the fact that sine is positive and cosine is negative in the second quadrant.

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