Question

Find cot theta if csc theta= the square root of 5/2 and tan theta>0

Answer 1

Since
`\cot^2\theta+1=\csc^2\theta`, you have


`\cot^2\theta=\left(\frac{\sqrt5}2\right)^2-1=\frac14`

`\cot\theta=\pm√(\frac14)=\pm\frac12`

Since
`\tan\theta>0`, and
`\cot\theta=\frac1{\tan\theta}`, you know that
`\cot\theta` is also positive, which means


`\cot\theta=\frac12`