JAMB 1998 · UME · Q36✱✱

Trigonometric graphs

For what value of $x$ does $6\sin(2x - 25)^\circ$ attain its maximum value in the range $0^\circ \le x \le 180^\circ$ ?

Worked solution (try it first)

$\sin\theta$ reaches its maximum value, 1, when $\theta = 90^\circ$ .
So set $2x - 25 = 90$ .
Add 25 to both sides: $2x = 115$ .
Divide by 2: $x = 57\frac12$ , option C.
The next maximum, $2x - 25 = 450$ , gives $x = 237\frac12$ , outside the range.

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