given csc x =-3 and tan x> 0 find cosx

Answer 1

Hi Brooke,

csc(x) is equal to 1/sin(x). This means in this problem that sin(x) = -1/3.

The only quadrant where sin(x) is negative and tan(x) is positive is the 3rd quadrant.

Since sin²(x) + cos²(x) = 1, then

(-1/3)² + cos²(x) = 1

1/9 + cos²(x) = 1

cos²(x) = 8/9

cos(x) = ± sqrt(8/9)

Since we are in the 3rd quadrant, then the negative answer is correct, which simplifies to -2/3 * sqrt(2).

Please let me know if I can be more helpful, thanks!

Joe