Question

find the exact value.
cos \frac{9\pi}{4}
type + or -
? \frac{\sqrt{\square}}{\square}

Explanation:

Step1: Find the coterminal angle

Since \(2\pi\) is the period of the cosine function, we can find a coterminal angle of \(\frac{9\pi}{4}\) by subtracting \(2\pi\).
\(\frac{9\pi}{4}-2\pi=\frac{9\pi}{4}-\frac{8\pi}{4}=\frac{\pi}{4}\)
So, \(\cos\frac{9\pi}{4}=\cos\frac{\pi}{4}\)

Step2: Determine the sign

The angle \(\frac{\pi}{4}\) is in the first - quadrant. In the first - quadrant, the cosine function is positive.

Step3: Recall the value of \(\cos\frac{\pi}{4}\)

We know that \(\cos\frac{\pi}{4}=\frac{\sqrt{2}}{2}\)

Answer:

\(+\frac{\sqrt{2}}{2}\)