Question

question 1 (1 point)
given the trigonometric function ( y = \tan x ), find the ( x )-coordinate of the point ( left( \frac { 3 pi } { 4 },?
ight) ).
( \bigcirc ) a) ( - 1 )
( \bigcirc ) b) ( sqrt { 2 } )
( \bigcirc ) c) ( \frac { 1 } { sqrt { 2 } } )
( \bigcirc ) d) 1

Explanation:

Step1: Use the tangent formula

We know that \(\tan(A + B)=\frac{\tan A+\tan B}{1 - \tan A\tan B}\). Also, \(\frac{3\pi}{4}=\pi-\frac{\pi}{4}\), and \(\tan(\pi - \alpha)=-\tan\alpha\).

Step2: Calculate \(\tan\frac{3\pi}{4}\)

Since \(\tan\frac{\pi}{4} = 1\), then \(\tan\frac{3\pi}{4}=\tan(\pi-\frac{\pi}{4})=-\tan\frac{\pi}{4}\).
Substitute \(\tan\frac{\pi}{4} = 1\) into the formula, we get \(\tan\frac{3\pi}{4}=- 1\).

Answer:

A. -1