Question

pi/6 is the reference angle for:
3pi/6
5pi/6
13pi/6
8pi/6

Answer 1

The answer is \[\frac{ 13\pi }{ 6 }\]The reason is because \[\frac{ \pi }{ 6 }\] = 15 degrees, which means that the answer has to be 15 degrees passed a quadrant.
In this case, \[\frac{ 13\pi }{6 }\] = 195 degrees. which is 15 degrees passed 180 degrees.

Answer 2

ok but there is more than 1 answer

Answer 3

Hm...maybe we can use elimination then. We know the first two can't be the answer because they themselves are reference angles because first two<90 degrees.

Answer 4

Anything in the first quadrant is considered a reference angle.

Answer 5

Hopefully that helps

Answer 6

Take each answer choice and find out which quadrant it is.
a) 3(pi)/6 = pi/2 (or 90 degrees) which is along the y-axis. Since it is not on any of the quadrants it does not have a reference angle.
b) 5(pi)/6 is greater than 3(pi)/6 and less than 6(pi)/6. That is, it is in between (pi)/2 and (pi). In other words it is in the second quadrant.
The reference angle is the angle the radius make with the x-axis.
Therefore, in second quadrant, the reference angle is (pi) - x = (pi) - 5(pi)/6 =
{ 6(pi) - 5(pi) } / 6 = (pi)/6. Thus, pi/6 is the reference angle for 5(pi)/6.
c) 13pi/6 is (12pi + pi)/6 = 2(pi) + pi/6. 2(pi) is one full rotation. Therefore, we are left with pi/6 which is the angle made with the x-axis. Therefore, pi/6 is a reference angle for 13pi/6.
d) 8pi/6 = 4pi/3 = (3pi + pi)/3 = pi + pi/3. This is in the third quadrant where the reference angle is x = pi. pi + pi/3 - pi = pi/3. Therefore, pi/6 is NOT a reference angle for 8pi/6.