Question

Evaluate each of the following:

$si{n}^2{60}^{\circ }$ + $si{n}^2{45}^{\circ }$ + $si{n}^2{60}^{\circ }$ + $si{n}^2{90}^{\circ }$

Answer 1

sin ${30}^{\circ }$ = $\frac{1}{2}$

sin ${45}^{\circ }$ = $\frac{1}{\sqrt{2}}$

sin ${60}^{\circ }$ = $\frac{\sqrt{3}}{2}$

sin ${90}^{\circ }$ = 1

$si{n}^2{60}^{\circ }$ + $si{n}^2{45}^{\circ }$ + $si{n}^2{60}^{\circ }$ + $si{n}^2{90}^{\circ }$

= ($\frac{1}{2}{)}^2$ + ($\frac{1}{\sqrt{2}}{)}^2$ + ($\frac{\sqrt{3}}{2}{)}^2$ + 1

= $\frac{1}{4}$ + $\frac{1}{2}$ + $\frac{3}{4}$ + 1

= $\frac{5}{2}$