Question

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

Answer 1

A

Explanation:

Answer 2

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

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