Answer:
The reference angle of 315 degree or \(\frac{7\pi}{4}\) is 45 degrees.
\(\tan 315=-1\)
Step-by-step explanation:
Given : The measure of angle \(\theta\) is \(\frac{7\pi}{4}\).
To find : The measure of its reference angle is __°, and tan θ is __ ?
Solution :
The measure of angle \(\theta=\frac{7\pi}{4}\)
To get reference angle we convert radian into degree by multiplying \(\frac{180}{\pi}\)
\(\theta=\frac{7\pi}{4}\times \frac{180}{\pi}\)
\(\theta=\frac{7\times 180}{4}\)
\(\theta=315^\circ\)
Reference angle is the angle between x-axis and the terminal side of given angle.
The terminal side of angle 315 is lying in 4th quadrant.
The angle between x-axis and its terminal side is 360-315 = 45 degrees
The reference angle of 315 degree or \(\frac{7\pi}{4}\) is 45 degrees.
Now, \(\tan 315=\tan(360-45)\)
\(\tan 315=-\tan(45)\) (tan is negative in 4th quadrant)
\(\tan 315=-1\)
