use the unit circle to find $sin^{-1}(\frac{s...
use the unit circle to find $sin^{-1}(\frac{sqrt{3}}{2})$ in degrees. remember that the domain of inverse sine is limited to quadrants i and iv (the right side of the unit circle).\n\na. $225^{circ}$\nb. $0^{circ}$\nc. $60^{circ}$\nd. $330^{circ}$
Answer
# Explanation:
## Step1: Recall sine - value on unit circle
We know that $\sin\theta=\frac{y - coordinate}{radius}$ on the unit circle ($radius = 1$). We need to find $\theta$ such that $\sin\theta=\frac{\sqrt{3}}{2}$ and $\theta$ is in quadrants I or IV.
## Step2: Identify angle in quadrant I
In the unit - circle, for $\theta$ in quadrant I, when $\sin\theta=\frac{\sqrt{3}}{2}$, $\theta = 60^{\circ}$ since for the angle $\theta = 60^{\circ}$ (or $\frac{\pi}{3}$ radians), the coordinates on the unit circle are $(\cos60^{\circ},\sin60^{\circ})=(\frac{1}{2},\frac{\sqrt{3}}{2})$.
## Step3: Check other options
Option a: $\sin225^{\circ}=-\frac{\sqrt{2}}{2}$, option b: $\sin0^{\circ}=0$, option d: $\sin330^{\circ}=-\frac{1}{2}$.
# Answer:
C. $60^{\circ}$