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,

$\begin{gathered} \Rightarrow1+(\frac{1}{tan^2\theta})=csc^2\theta \\ \Rightarrow1+1=csc^2\theta \\ \Rightarrow csc\theta=\sqrt{2};0\degree\leq\theta\leq90\degree \end{gathered}$

Then, the answer is csc(θ)=sqrt(2)