question 1 (mandatory) (1 point)\nthe graph of $y = 1$ intersects the graph of $y=\tan x$ at\na)…

question 1 (mandatory) (1 point)\nthe graph of $y = 1$ intersects the graph of $y=\tan x$ at\na) $\frac{pi}{4}$\nb) $\frac{pi}{2}$\nc) $pi$\nd) $\frac{pi}{3}$

question 1 (mandatory) (1 point)\nthe graph of $y = 1$ intersects the graph of $y=\tan x$ at\na) $\frac{pi}{4}$\nb) $\frac{pi}{2}$\nc) $pi$\nd) $\frac{pi}{3}$

Answer

Explanation:

Step1: Set the equations equal.

Set $\tan x=1$.

Step2: Recall tangent - value.

We know that $\tan x=\frac{\sin x}{\cos x}$, and $\tan x = 1$ when $\sin x=\cos x$. In the interval $(-\frac{\pi}{2},\frac{\pi}{2})$, the value of $x$ for which $\tan x = 1$ is $x = \frac{\pi}{4}$ since $\tan\frac{\pi}{4}=\frac{\sin\frac{\pi}{4}}{\cos\frac{\pi}{4}}=\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = 1$.

Answer:

A. $\frac{\pi}{4}$