Determine the other two trig ratios

Question

If tan theta < 0 and sin theta = 8/17, what are the exact values of the other two trig ratios? What is the reference angle and terminal angle?

Answer 1

8 & 17 OUGHT to bring to mind the classic right triangle 8-15-17. Place this reference triangle in the second quadrant, because that's the quadrant in which sines are positive but tangents are negative.

 

Thus one sees, instantly, that tan θ = -8/15, cos  θ = -15/17, and so forth.