Question

Which of the following could be used as a reference angle for 15 pi / 4

Answer 1

Answer:

$\frac{\pi }{4}$ could be used as a reference angle for $\frac{15\pi }{4}$.

Step-by-step explanation:

Given the trigonometric expression

$\frac{15\pi }{4}$

In order to find the reference angle for $\frac{15\pi }{4}$, find an angle that is positive, less than $2\pi$, and coterminal with

Subtract  $2\pi$ from  $\frac{15\pi }{4}$.

$\frac{15\pi }{4} -2\pi$

The resulting angle of $\frac{7\pi }{4}$ is positive, less than $2\pi$, and coterminal with   $\frac{15\pi }{4}$.

$\frac{7\pi }{4}$

Since the angle $\frac{7\pi }{4}$ is in the fourth quadrant, subtract

$2\pi-\frac{7\pi }{4}=\frac{\pi }{4}$

Therefore, $\frac{\pi }{4}$ could be used as a reference angle for $\frac{15\pi }{4}$.

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Answer 2

The reference angle = $\frac{\pi}{4}$.

Note that     $\frac{15\pi}{4}$  $\frac{15\pi}{4}=3.75\pi$ lies in the 4th quadrant and it is close to  $4\pi$.

To find the reference angle of  $\frac{15\pi}{4}$  we will subtract it from $4\pi$.

So, the reference angle is:

$4\pi-\frac{15\pi}{4}=\frac{\pi}{4}$

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