Find the exact value of the trigonometric function given that sin u = 5/13 and cos v = -3/5. (Both u and v are in Quadrant II.)

Question

Find csc(u-v).

First of all, I drew the triangles of u and v. Also, I know the formula of sin(u-v) is sin u * cos v - cos u * sin v. However, I am confused of what you do when you have csc(u-v). Would you do csc u * sec v - sec u * csc v?

Thanks.

Reiny · Accepted Answer

no, that is wishful thinking. csc(u-v) = 1/sin(u-v) so work out the sin(u-v) according to your formula, the take the reciprocal of your final fraction.

Vincent · Answer

Okay, I worked sin(u-v) out and I got 33/65. Would I then flip it over and get 65/33 as my final answer?

Reiny · Answer

yes, that is also what I got (and I checked it by finding the actual angles)

Vincent · Answer

Okay thanks for your help!