find the exact value. tan 3π/4

Explanation:

Step1: Convert angle to degree

We know that $\pi$ radians $ = 180^{\circ}$, so $\frac{3\pi}{4}=\frac{3\times180^{\circ}}{4}=135^{\circ}$.

Step2: Use the tangent formula

$\tan\theta=\frac{\sin\theta}{\cos\theta}$. For $\theta = 135^{\circ}$, $\sin135^{\circ}=\sin(180^{\circ}-45^{\circ})=\sin45^{\circ}=\frac{\sqrt{2}}{2}$, $\cos135^{\circ}=\cos(180^{\circ}-45^{\circ})=-\cos45^{\circ}=-\frac{\sqrt{2}}{2}$. Then $\tan135^{\circ}=\frac{\sin135^{\circ}}{\cos135^{\circ}}=\frac{\frac{\sqrt{2}}{2}}{-\frac{\sqrt{2}}{2}}=- 1$.

Answer:

$-1$