Question

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

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

Short answer

The exact value of$\frac{\sin \left(-{20}^o\right)}{\cos \left({380}^o\right)}+\tan \left({200}^o\right)is0.$

Step-by-step solution

Given information

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

Use periodicity property of trigonometric functionssinθ+2π=sinθcosθ+2π=cosθtanθ+π=tanθ

We get,

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

Conclusion

The exact value of$\frac{\sin \left({20}^o\right)}{\cos \left({20}^o\right)}+\tan \left({20}^o\right)is0.$