use the (x,y) coordinates in the figure to find the value of the trigonometric function at the indicated…
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.
Answer
Explanation:
Step1: Recall unit - circle definition of sine
The sine of an angle $\theta$ in the unit - circle is the $y$ - coordinate of the point on the unit - circle corresponding to the angle $\theta$.
Step2: Locate the angle $\frac{\pi}{6}$ on the unit - circle
The angle $\frac{\pi}{6}$ (or $30^{\circ}$) on the unit - circle has the coordinates $\left(\frac{\sqrt{3}}{2},\frac{1}{2}\right)$.
Step3: Determine the value of $\sin\frac{\pi}{6}$
Since $\sin\theta=y$ for a point $(x,y)$ on the unit - circle corresponding to the angle $\theta$, for $\theta = \frac{\pi}{6}$, we have $\sin\frac{\pi}{6}=\frac{1}{2}$.
Answer:
A. $\sin\frac{\pi}{6}=\frac{1}{2}$