Question

Given tan θ = 1 and 0 ≤ θ ≤ 90°, what is csc θ?

Answer 1

In general,

`\begin{gathered} 1+cot^2\theta=csc^2\theta \\ and \\ tan\theta=cot\theta \end{gathered}`

Therefore,

`\begin{gathered} \Rightarrow1+((1)/(tan^2\theta))=csc^2\theta \\ \Rightarrow1+1=csc^2\theta \\ \Rightarrow csc\theta=√(2);0\degree\leq\theta\leq90\degree \end{gathered}`

Then, the answer is csc(θ)=sqrt(2)