Question

Find the exact value of each expression. Do not use a calculator.

$\frac{\sin \left(-{40}^{°}\right)}{\sin {40}^{°}}$.

Short answer

The exact value of the expression$\frac{\sin \left(-{40}^{°}\right)}{\sin {40}^{°}}$is,$-1$.

Step-by-step solution

Step 1 Given expression is,

$\frac{\sin \left(-{40}^{°}\right)}{\sin {40}^{°}}$.

The objective is, we need to find the exact value for the given expression without using the calculator.

Step 2 We know that,

$$\begin{gathered} \sin \left(-\theta \right)=\sin \theta \\ \sin \left(-{40}^{°}\right)=\sin {40}^{°} \end{gathered}$$

So, the given expression becomes,

$$\begin{gathered} \frac{\sin \left(-{40}^{°}\right)}{\sin {40}^{°}}=\frac{-\sin {40}^{°}}{\sin {40}^{°}} \\ =-1 \end{gathered}$$