Consider the trigonometric equation .

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

Problem

Consider the trigonometric equation sin⁡x=12\sin x = \dfrac{1}{2}. (i) Determine all values of xx that satisfy the equation in the interval 0≤x<2π0 \le x < 2\pi. (ii) Write the general solution of the equation for all real xx. (iii) Explain, using the periodic nature and quadrant–wise sign of the sine function, why the expression obtained in part (ii) lists every possible real solution of the equation.

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