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

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