Find cotangent of theta if cosecant of theta equals 8/3?

Question

If you use the pythagorean identities, and say that cotangent ^2 = cosecant ^2 -1, how do you solve?

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Answer 1 · 2018-04-07T23:34:40

$cot θ = \frac{\sqrt{55}}{3}$ $cottheta=sqrt55/3$

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${cot}^{2} θ = {csc}^{2} θ - 1$ $cot^2theta=csc^2theta-1$

${cot}^{2} θ = {(\frac{8}{3})}^{2} - 1 = \frac{64}{9} - 1 = \frac{55}{9}$ $cot^2theta=(8/3)^2-1=64/9-1=55/9$

$cot θ = \frac{\sqrt{55}}{3}$ $cottheta=sqrt55/3$