Question

use the (x,y) coordinates in the figure to find the value of the trigonometric function at the indicated real number, t, or state that the expression is undefined. sin(π/6) select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. sin(π/6)=□ (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) b. the expression is undefined.

Explanation:

Step1: Recall sine - unit circle definition

The sine of an angle $t$ in the unit - circle is given by the $y$ - coordinate of the point on the unit circle corresponding to the angle $t$.

Step2: Locate the angle $\frac{\pi}{6}$ on the unit circle

The angle $t = \frac{\pi}{6}$ corresponds to the point $(\frac{\sqrt{3}}{2},\frac{1}{2})$ on the unit circle.

Step3: Determine the value of $\sin\frac{\pi}{6}$

Since $\sin t$ is the $y$ - coordinate of the point on the unit circle corresponding to the angle $t$, for $t=\frac{\pi}{6}$, $\sin\frac{\pi}{6}=\frac{1}{2}$.

Answer:

A. $\sin\frac{\pi}{6}=\frac{1}{2}$