Suppose that $ is an angle with csc$=-12/5 and $ is not in the third quadrant. Compute the exact value of Tan$. You don’t have to rationalize the denominator.

Question

$ represents theta symbol. I think the answer is -5/rad119

Answer 1

call the angle "x"

cscx=-12/5

cscx=1/sinx

1/sinx=-12/5

sinx=-5/12

using the Pythagorean Theorem to find the adjacent side...

sin is opposite/hypotenuse so we are missing the adjacent side

12^2=(-5)^2+a^2 where a=adjacent side

144=25+a^2

a^2=119

a=√119

tanx=opposite/adjacent

tanx=-5/√119