Question

use the special triangles on the unit circle to determine $\theta$ in degrees when $sin\theta=\frac{sqrt{3}}{2}$. (1 point) 45° 90° 30° 60°

Explanation:

Step1: Recall sine - value in special triangles

In a 30 - 60 - 90 special right - triangle on the unit circle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Analyze the 30 - 60 - 90 triangle

For a 30 - 60 - 90 triangle with hypotenuse $r = 1$ (unit circle), if $\theta=60^{\circ}$, the opposite side to the $60^{\circ}$ angle has length $\frac{\sqrt{3}}{2}$ and $\sin60^{\circ}=\frac{\sqrt{3}}{2}$. For $\theta = 30^{\circ}$, $\sin30^{\circ}=\frac{1}{2}$, for $\theta = 45^{\circ}$, $\sin45^{\circ}=\frac{\sqrt{2}}{2}$, and for $\theta = 90^{\circ}$, $\sin90^{\circ}=1$.

Answer:

D. $60^{\circ}$