use the reference angle to find the exact value of each expression. do not use a calculator. sin 4π select…
use the reference angle to find the exact value of each expression. do not use a calculator. sin 4π select the correct choice below and fill in any answer boxes in your choice. a. sin 4π = (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.) b. the answer is undefined.
Answer
Explanation:
Step1: Recall the period of sine function
The period of $y = \sin(x)$ is $2\pi$, so $\sin(4\pi)=\sin(2\times2\pi)$. Since $\sin(x + 2k\pi)=\sin(x)$ for any real - number $x$ and integer $k$, here $x = 0$ and $k = 2$, then $\sin(4\pi)=\sin(0)$.
Step2: Find the value of $\sin(0)$
We know from the unit - circle definition that for an angle $\theta$ in standard position, $\sin\theta=y$ where $(x,y)$ is the point on the unit - circle corresponding to $\theta$. When $\theta = 0$, the point on the unit - circle is $(1,0)$, so $\sin(0)=0$.
Answer:
A. $\sin 4\pi = 0$