Consider the function .

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

Problem

Consider the function y=sin⁡xy=\sin x. (i) Sketch one continuous graph of y=sin⁡xy=\sin x for the interval −π≤x≤3π-\pi \le x \le 3\pi. Mark clearly all xx-intercepts, maximum and minimum points. (ii) Using the sketch, verify geometrically that sin⁡(−x)=−sin⁡x\sin(-x)= -\sin x for all real xx. (iii) From your graph identify the intervals, within −π≤x≤3π-\pi \le x \le 3\pi, in which the function is increasing and those in which it is decreasing.

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