Question

question 7 (1 point)
the graph of ( y = 1 ) intersects the graph of ( y = \tan x ) at
( \bigcirc ) a) ( pi )
( \bigcirc ) b) ( \frac{pi}{4} )
( \bigcirc ) c) ( \frac{pi}{3} )
( \bigcirc ) d) ( \frac{pi}{2} )

Explanation:

Step1: Solve the equation \(\tan x = 1\)

We know that the general solution of the equation \(\tan x=\tan\alpha\) is \(x = n\pi+\alpha\), \(n\in\mathbb{Z}\).
Since \(\tan x = 1=\tan\frac{\pi}{4}\), then \(x=n\pi+\frac{\pi}{4}\), \(n\in\mathbb{Z}\).
When \(n = 0\), \(x=\frac{\pi}{4}\)

Answer:

B. \(\frac{\pi}{4}\)