Question

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

Θ' = negative pi over 6; sine and cosine are positive, tangent is negative.
Θ' = 5 pi over 6; sine and tangent are positive, cosine is negative
Θ' = pi over 6; sine is positive, cosine and tangent are negative
Θ' = negative 5 pi over 6; sine is positive, cosine and tangent are negative

PLEASE someone help me. Thank you.

Answer 1

This angle is in the second quadrant of the unit circle.  That is its in between 90 and 180 degrees ( pi/2 and pi radians.
In this quadrant only the sine is positive.

Now in the UK we would say that the reference angle  is pi - 5pi/6  = pi/6
and the correct answer is C.  I notice that there are some differences between UK and US trig standards so I can only give the UK answer.