Question

question 3 of 25
on a unit circle, the terminal point of \\( \theta \\) is \\( \left( \frac { \sqrt { 2 } } { 2 }, \frac { \sqrt { 2 } } { 2 } \
ight) \\). what is \\( \theta \\) if \\( 0 ^ { \circ } \leq \theta < 360 ^ { \circ } \\) ?
a. \\( 15 ^ { \circ } \\)
b. \\( 60 ^ { \circ } \\)
c. \\( 45 ^ { \circ } \\)
d. \\( 30 ^ { \circ } \\)

Explanation:

Step1: Recall unit circle coordinates

On a unit circle, terminal point is $(\cos\theta, \sin\theta)$.

Step2: Match coordinates to angle

Given $(\cos\theta, \sin\theta)=(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$. We know $\cos45^\circ=\frac{\sqrt{2}}{2}$ and $\sin45^\circ=\frac{\sqrt{2}}{2}$.

Answer:

C. 45°