Question

find the exact value.
tan \frac{3\pi}{4}

Explanation:

Step1: Determine the reference angle

The angle \(\frac{3\pi}{4}\) is in the second quadrant. The reference angle \(\theta'\) for \(\theta=\frac{3\pi}{4}\) is \(\pi-\frac{3\pi}{4}=\frac{\pi}{4}\).

Step2: Use the tangent formula for the second quadrant

In the second quadrant, \(\tan\theta =-\tan\theta'\). Since \(\tan\frac{\pi}{4} = 1\), then \(\tan\frac{3\pi}{4}=-\tan\frac{\pi}{4}\).

Answer:

\(- 1\)