Question

Given that cosθ = - and θ is in the second quadrant, find cscθ.

Answer 1

Since sin²x+cos²x=1, we can plug (-12/13) for cos(x) to get (-12/13)²+sin²x=1 
= 144/169+sin²x=1. Subtracting 144/169 from both sides, we get 25/169=sin²x. Square rooting both sides, we get 5/13 as sinx (since √25=5 and √169=13,as well as that it's in quadrant 2 - if it was in quadrant 3 or 4, it would be -5/13). Since cscx=1/sinx, we can plug (5/13) in for sinx to get 13/5 as our answer