Question

Check all that apply. (pi/6) is the reference angle for:
1. 8pi/6
2.5pi/6
3.3pi/6
4.13pi/6

Answer 1

Answer:

$\frac{5\pi}{6}$ and $\frac{13\pi}{6}$ are the reference angles.

Step-by-step explanation:

Reference angle is the angle which makes from the terminal side of the x-axis.

You can see  the attachment for the angles which are reference angles.

Angle A is equal to $2\pi+\theta$

B is equal to $\pi-\theta$

C is equal to $\pi+\theta$

D is equal to $2\pi-\theta$

We will apply all four operations of A,B,C and D

A=$2\pi+\frac{\pi}{6}=\frac{13\pi}{6}$

B= $\pi-\frac{5\pi}{6}=\frac{5\pi}{6}$

C=$\pi+\frac{\pi}{6}=\frac{7\pi}{6}$

D=$2\pi-\frac{\pi}{6}=\frac{11\pi}{6}$

Therefore, Option 2 and 4th are correct from the given options.

$\frac{5\pi}{6}$ and $\frac{13\pi}{6}$

Answer 2

You can use the definition of the reference angle to find the result.

The reference angle for  $\dfrac{\pi}{6}$  is given by  $\dfrac{\pi}{6}$

What is a reference angle of a given angle?

Think of reference angle as the minimum angle reaching from x axis to the terminal side of the given angle. Thus, if suppose the angle is 180 degrees, then it is overlapping on x axis, thus, the reference angle is 0.

If the angle is 135 degrees, we can reach it by shortcut from other side of x axis with only 45 degree walk. Thus, reference angle is 45 degrees.(see diagram attached below)

If its right angle, there is no choice, but only right angle to be as the reference angle.

Since the given angle is $\dfrac{\pi}{6} = 30^\circ < 90^\circ$, thus it is already acute version and thus, its reference angle will measure the same.

The reference angle for  $\dfrac{\pi}{6}$  is given by  $\dfrac{\pi}{6}$

Learn more about reference angles here:

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