Sketching the sine curve over four complete periods.

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

Problem

Sketching the sine curve over four complete periods. (i) Prepare a table of at least eight ordered pairs (x,sin⁡x)(x,\sin x) that are sufficient to sketch the graph of y=sin⁡xy=\sin x for x∈[−2π,2π]x\in[-2\pi,2\pi]. Choose your xx-coordinates at equal intervals. (ii) Using the table, draw a neat and properly scaled sketch of the graph on a radian horizontal axis. Clearly label the intercepts and the maximum and minimum points. (iii) From your sketch, write down the number of solutions of sin⁡x=12\sin x=\dfrac{1}{2} lying in the interval [−2π,2π][-2\pi,2\pi] and list them.

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