Question

Use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator.

$\sin {180}^{\mathrm{o}}\csc {80}^{\mathrm{o}}$

Short answer

The simplified form can be found as 1.

Step-by-step solution

Step 1. Given Information

Given that the trigonometric expression is $\sin {180}^{\mathrm{o}}\csc {80}^{\mathrm{o}}.$To find the exact values using given expression by fundamental identity.

Step 2. Value of the expression

On using fundamental identity,

$$\begin{gathered} \mathrm{csc\vartheta \vartheta }=\frac{1}{\mathrm{sin\theta }} \\ \sin {180}^{\mathrm{o}}\csc {80}^{\mathrm{o}}=\sin {80}^{\mathrm{o}}\frac{1}{\sin {80}^{\mathrm{o}}} \\ \sin {180}^{\mathrm{o}}\csc {80}^{\mathrm{o}}=1 \end{gathered}$$