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

The reference angle for (pi/6) is determined by finding which of the given angles are coterminal with (pi/6).

Step-by-step explanation:

The reference angle is the acute angle between the terminal side of an angle in standard position and the x-axis. To find the reference angle of (pi/6), we need to determine which of the given angles are coterminal with (pi/6).

1. (pi/6) = 30 degrees. The reference angle for 30 degrees is 30 degrees itself, so (pi/6) is the reference angle for this angle.
2. (5pi/6) = 150 degrees. The reference angle for 150 degrees is 30 degrees, so (pi/6) is not the reference angle for this angle.
3. (3pi/6) = 90 degrees. The reference angle for 90 degrees is 0 degrees, so (pi/6) is not the reference angle for this angle.
4. (13pi/6) = 390 degrees. The reference angle for 390 degrees is 30 degrees, so (pi/6) is the reference angle for this angle.

Therefore, (pi/6) is the reference angle for angles 1 and 4.

Answer 2

`(5\pi)/(6)` and
`(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+(\pi)/(6)=(13\pi)/(6)`

B=
`\pi-(5\pi)/(6)=(5\pi)/(6)`

C=
`\pi+(\pi)/(6)=(7\pi)/(6)`

D=
`2\pi-(\pi)/(6)=(11\pi)/(6)`

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

`(5\pi)/(6)` and
`(13\pi)/(6)`