Is in the 4th forth quadrant so the reference angle can be solve using
A = 2π - 7π/4
Answer:
The reference angle of 315 degree or [tex]\frac{7\pi}{4}[/tex] is 45 degrees.
[tex]\tan 315=-1[/tex]
Step-by-step explanation:
Given : The measure of angle [tex]\theta[/tex] is [tex]\frac{7\pi}{4}[/tex].
To find : The measure of its reference angle is __°, and tan θ is __ ?
Solution :
The measure of angle [tex]\theta=\frac{7\pi}{4}[/tex]
To get reference angle we convert radian into degree by multiplying [tex]\frac{180}{\pi}[/tex]
[tex]\theta=\frac{7\pi}{4}\times \frac{180}{\pi}[/tex]
[tex]\theta=\frac{7\times 180}{4}[/tex]
[tex]\theta=315^\circ[/tex]
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 [tex]\frac{7\pi}{4}[/tex] is 45 degrees.
Now, [tex]\tan 315=\tan(360-45)[/tex]
[tex]\tan 315=-\tan(45)[/tex] (tan is negative in 4th quadrant)
[tex]\tan 315=-1[/tex]
