Question

If cot theta = 2/3, what is the value of csc theta?

Answer 1

Hi,$\dfrac{2}{3} =cotg\ \theta =\dfrac{cos\ \theta}{sin\ \theta}\\\\ \Rightarrow\ 2*sin\ \theta=3*cos\ \theta\\\\ \Rightarrow\ 2*sin\ \theta=3* \sqrt{1-sin^2\ \theta} \\\\ \Rightarrow\ 4*sin^2\ \theta=9* (1-sin^2\ \theta}) \\\\ \Rightarrow\ 13*sin^2\ \theta=9) \\\\ \Rightarrow\ sin\ \theta= \dfrac{3}{ \sqrt{13} } \\\\ \Rightarrow\ \dfrac{1}{sin\ \theta}=cosec\ \theta= \dfrac{ \sqrt{13} }{3} \\\\ \boxed{cosec\ \theta= \dfrac{ \sqrt{13} }{3} }$

Maybe "cosec a, cotg a" (in  french) is written "csc a,cot a" in american

Answer 2

Sqrt 13/3

There is a great explanation at https://socratic.org/questions/if-cot-theta-2-3-what-is-the-value-of-csc-theta