1. use the figure to find the value of tan(5π/4). tan(5π/4) = enter your next step here

Explanation:

Step1: Recall tangent formula

$\tan\theta=\frac{\sin\theta}{\cos\theta}$.

Step2: Find $\sin(\frac{5\pi}{4})$ and $\cos(\frac{5\pi}{4})$ from unit - circle

From the unit - circle, for $\theta = \frac{5\pi}{4}$, $\sin(\frac{5\pi}{4})=-\frac{\sqrt{2}}{2}$ and $\cos(\frac{5\pi}{4})=-\frac{\sqrt{2}}{2}$.

Step3: Calculate the tangent value

$\tan(\frac{5\pi}{4})=\frac{\sin(\frac{5\pi}{4})}{\cos(\frac{5\pi}{4})}=\frac{-\frac{\sqrt{2}}{2}}{-\frac{\sqrt{2}}{2}} = 1$.

Answer:

$1$