Q.88 - 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:  

$\frac{\sin \left({70}^o\right)}{\cos \left({430}^o\right)}+\tan \left(-{70}^o\right)$

Step-by-Step Solution

Answer

The exact value of $\frac{\sin \left({70}^o\right)}{\cos \left({430}^o\right)}+\tan \left(-{70}^o\right) is 0.$

Step 1: Given information

We are given a equation $\frac{\sin \left({70}^o\right)}{\cos \left({430}^o\right)}+\tan \left(-{70}^o\right)$

Step 2: use the periodicity of trigonometric function cos θ + 2 π = cos θ tan - θ = - tan θ

We have,

$$\begin{gathered} \frac{\sin \left({70}^o\right)}{\cos \left({430}^o\right)}+\tan \left(-{70}^o\right) \\ \frac{\sin \left({70}^o\right)}{\cos \left({70}^o\right)}-\tan \left({70}^o\right) \\ \frac{\sin \left({70}^o\right)}{\cos \left({70}^o\right)}-\frac{\sin \left({70}^o\right)}{\cos \left({70}^o\right)} \\ =0 \end{gathered}$$

Step 3: Conclusion

The exact value of $\frac{\sin \left({70}^o\right)}{\cos \left({70}^o\right)}-\tan \left({70}^o\right) is 0.$