Answer:
tanx = [tex]\frac{\sqrt{3} }{3}[/tex]
Step-by-step explanation:
cscx = -2, and because csc is = 1/sin, you can say that sinx = -1/2
If sinx = -1/2, you can draw a triangle and label each side.
From there, you'll know that the opposite side is -1 and the hypotenuse is 2. You can then use the Pythagorean Theorem to find the adjacent side, which is equal to [tex]-\sqrt{3}[/tex].
Finally, you can find the tangent and see that it is [tex]\frac{-1}{-\sqrt{3} }[/tex].
To simplify, you can cancel the negative signs and make it positive. You can either keep it as [tex]\frac{1}{\sqrt{3} }[/tex] or rationalize it and get [tex]\frac{\sqrt{3} }{3}[/tex].
Hope I helped :)
