Question

When Θ = 5 pi over 6, what are the reference angle and the sign values for sine, cosine, and tangent?

Answer 1

Answer: 0’ = pie/6; sine is positive, cosine and tangent are negative

Answer 2

Ф =5π/6
The reference angle is the smallest angle that the terminal side of the angle makes with the x-axis.

Given that here π/2 < Ф < π, the angle is in the second quadrant.

In the second quadrant the signs are:

sine positive
cosine negative
tangent negative.

Furthermore, the reference angle is π - Ф = π - 5π/6 = π/6.

Then,

sin Ф = sin π/6 = 1/2
cos Ф = - cos π/6 = -√(3) / 2
tan Ф = - tan π/6 = -√(3) /3