Question

Solve the following equation in the interval [0, 2 π]. Note: Give the answer as a multiple of π. Do not use decimal numbers. The answer should be a fraction or an integer. Note that π is already included in the answer so you just have to enter the appropriate multiple. E.g. if the answer is π/2 you should enter 1/2. If there is more than one answer enter them separated by commas. (sin(t))^2=3/4

Answer 1

$\bf [sin(t)]^2=\cfrac{3}{4}\implies sin^2(t)=\cfrac{3}{4}\implies sin(t)=\pm\sqrt{\cfrac{3}{4}} \\\\\\ sin(t)=\pm\cfrac{\sqrt{3}}{\sqrt{4}}\implies sin(t)=\pm\cfrac{\sqrt{3}}{2}\implies \measuredangle t= \begin{cases} \frac{\pi }{3}\\\\ \frac{2\pi }{3}\\\\ \frac{4\pi }{3}\\\\ \frac{5\pi }{3} \end{cases}$