Question

use the unit circle and the period of the function to evaluate the expression. write your answer as a simplified fraction, if necessary. select “undefined” if applicable. part: 0 / 3 part 1 of 3 (a) $cos\frac{9pi}{2}=square$ $\frac{square}{square}$ $sqrt{square}$ undefined

Explanation:

Step1: Recall the period of cosine function

The cosine function \(y = \cos(x)\) has a period of \(2\pi\), i.e., \(\cos(x)=\cos(x + 2k\pi)\) for any integer \(k\). We can rewrite \(\frac{9\pi}{2}\) as \(\frac{9\pi}{2}=4\pi+\frac{\pi}{2}\). Since \(4\pi = 2\times2\pi\), \(\cos(\frac{9\pi}{2})=\cos(4\pi+\frac{\pi}{2})=\cos(\frac{\pi}{2})\).

Step2: Use the unit - circle definition

On the unit - circle, for an angle \(\theta\), the \(x\) - coordinate of the point on the unit - circle corresponding to the angle \(\theta\) is \(\cos(\theta)\). For \(\theta=\frac{\pi}{2}\), the point on the unit - circle is \((0,1)\), so \(\cos(\frac{\pi}{2}) = 0\).

Answer:

0