Find the point $( x , y )$ on the unit circle that corresponds to the real number t. $$t = \frac { \pi } { 3 }$$
A)$t = \frac { \pi } { 3 }$ corresponds to the point $\left( - \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$.
B) $t = \frac { \pi } { 3 }$ corresponds to the point $\left( \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$.
C) $t = \frac { \pi } { 3 }$ corresponds to the point $\left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$.
D) $t = \frac { \pi } { 3 }$ corresponds to the point $\left( \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$.
E) $t = \frac { \pi } { 3 }$ corresponds to the point $\left( \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$.

Question

Find the point $( x , y )$ on the unit circle that corresponds to the real number t. $$t = \frac { \pi } { 3 }$$ 
A)$t = \frac { \pi } { 3 }$ corresponds to the point $\left( - \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$.
B) $t = \frac { \pi } { 3 }$ corresponds to the point $\left( \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$.
C) $t = \frac { \pi } { 3 }$ corresponds to the point $\left( \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$.
D) $t = \frac { \pi } { 3 }$ corresponds to the point $\left( \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$.
E) $t = \frac { \pi } { 3 }$ corresponds to the point $\left( \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$.

Quizplus · Accepted Answer

The point $(x, y)$ on the unit circle corresponding to $t = \frac{\pi}{3}$ is $\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$, as this angle is in the first quadrant where both sine and cosine are positive, and the sine of $\frac{\pi}{3}$ is $\frac{\sqrt{3}}{2}$ and the cosine is $\frac{1}{2}$.

Find the Point (x,y)( x , y )(x,y) On the Unit Circle That Corresponds to the Real Number

Find the Point $( x , y )$ On the Unit Circle That Corresponds to the Real Number