Q.87 - Precalculus Enhanced with Graphing Utilities

Question

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

$\frac{\sin \left(-{20}^o\right)}{\cos \left({380}^o\right)}+\tan \left({200}^o\right)$

Step-by-Step Solution

Answer

The exact value of $\frac{\sin \left(-{20}^o\right)}{\cos \left({380}^o\right)}+\tan \left({200}^o\right) is 0.$

Step 1: Given information

We are given a equation $\frac{\sin \left(-{20}^o\right)}{\cos \left({380}^o\right)}+\tan \left({200}^o\right)$

Step 2: Use periodicity property of trigonometric functions sin θ + 2 π = sin θ cos θ + 2 π = cos θ tan θ + π = tan θ

We get,

$$\begin{gathered} \frac{\sin \left(-{20}^o\right)}{\cos \left({380}^o\right)}+\tan \left({200}^o\right) \\ -\frac{\sin \left({20}^o\right)}{\cos \left({20}^o\right)}+\tan \left({20}^o\right) \\ -\frac{\sin \left({20}^o\right)}{\cos \left({20}^o\right)}+\frac{\sin \left({20}^o\right)}{\cos \left({20}^o\right)} \\ =0 \end{gathered}$$

Step 3: Conclusion

The exact value of $\frac{\sin \left({20}^o\right)}{\cos \left({20}^o\right)}+\tan \left({20}^o\right) is 0.$