use the figure of the first quadrant of the unit circle to find the exact circular function value. tan(π/4)…

Explanation:

Step1: Recall tangent - function formula

The formula for the tangent function is $\tan\theta=\frac{\sin\theta}{\cos\theta}$.

Step2: Find $\sin\frac{\pi}{4}$ and $\cos\frac{\pi}{4}$

From the unit - circle, for $\theta = \frac{\pi}{4}$, the coordinates of the corresponding point are $(\cos\frac{\pi}{4},\sin\frac{\pi}{4})=(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$. So, $\sin\frac{\pi}{4}=\frac{\sqrt{2}}{2}$ and $\cos\frac{\pi}{4}=\frac{\sqrt{2}}{2}$.

Step3: Calculate $\tan\frac{\pi}{4}$

Substitute $\sin\frac{\pi}{4}$ and $\cos\frac{\pi}{4}$ into the tangent formula: $\tan\frac{\pi}{4}=\frac{\sin\frac{\pi}{4}}{\cos\frac{\pi}{4}}=\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$.

Answer:

$1$