Question

Find the cosine of an angle in the second quadrant whose cosecant is 5/3.

A) 3/5
B) -3/5
C)-4/5
D) 4/5
E) -4/3

Answer 1

Sketch the triangle in QII.

csc(x) = 1/sin(x) = hypotenuse/opposite = 5/3

This is a 3-4-5 triangle so the adjacent side must be 4. ***however*** since we are in QII the cos is negative and the adjacent side is actually treated as -4 in the formula. From there it’s a straightforward cos(theta) = adjacent/hypotenuse calculation.