Question

find the exact values of the six trigonometric functions of the given angle. if any are not defined, say
ot defined.\ do not use a calculator. $\frac{25pi}{2}$
what is the value of $sin\frac{25pi}{2}$? select the correct choice and, if necessary, fill in the answer box to complete your choice.
a. $sin\frac{25pi}{2}=square$ (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)
b. the function is not defined.

Explanation:

Step1: Rewrite the angle

We can rewrite $\frac{25\pi}{2}$ as $\frac{24\pi + \pi}{2}=12\pi+\frac{\pi}{2}$. Since the sine - function has a period of $2\pi$, $\sin(12\pi+\frac{\pi}{2})=\sin\frac{\pi}{2}$.

Step2: Evaluate the sine - function

We know that for the unit - circle definition of the sine function, $\sin\theta = y$ coordinate of the point on the unit circle corresponding to the angle $\theta$. For $\theta=\frac{\pi}{2}$, the point on the unit circle is $(0,1)$, so $\sin\frac{\pi}{2}=1$.

Answer:

A. $\sin\frac{25\pi}{2}=1$