Question

In problems 11-26,use the fact that the trigonometric function are periodic to find the exact value of each expression. Do not use a calculator.

$\csc \left({450}^{\circ \hspace{0.17em}}\right)$

Short answer

The exact value is$1$.

Step-by-step solution

Step 1. Given information.  

We have:

$\csc \left({450}^{\circ \hspace{0.17em}}\right)$

Step 2. Find the exact value of trigonometric function.   

The function is $\csc \left({450}^{\circ \hspace{0.17em}}\right)$.

Formula used:

$csc\left(\theta +2\pi \right)=csc\theta$

Here, $\theta =90$

$$\begin{gathered} csc\left(90°+360°\right)=csc90° \\ =\frac{1}{\sin 90°} \\ =\frac{1}{1} \\ =1 \end{gathered}$$