find the exact value.\ncos \\frac{9\\pi}{4}\ntype + or -\n? \\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})