Note the answer must be positive because if sin>0, then csc > 0. There are two ways to do this problem. 1) Use a trig identity: [tex]csc^2 \theta = cot^2 \theta + 1[/tex] Sub in value for cot [tex]csc^2 \theta = (-\frac{21}{20})^2 + 1 \\ \\ csc^2 \theta = \frac{841}{400} \\ \\ csc \theta = \frac{\sqrt{841}}{\sqrt{400}} = \frac{29}{20}[/tex]
2) Use a right triangle and SOH CAH TOA cot = 1/tan = adjacent/opposite = -21/20 Therefore adjacent side = 21, opposite side = 20 Use pythagorean thm to find hypotenuse: [tex]\sqrt{21^2 + 20^2} = \sqrt{841} = 29 [/tex]
