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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 6: Q.88 (page 396)

use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator:
$\frac{\sin (70^{o})}{\cos (430^{o})} + \tan (- 70^{o})$

Short Answer

Expert verified

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

Step by step solution

01

Given information

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

02

use the periodicity of trigonometric function cosθ+2π=cosθtan-θ=-tanθ

We have,

$\frac{\sin (70^{o})}{\cos (430^{o})} + \tan (- 70^{o}) \frac{\sin (70^{o})}{\cos (70^{o})} - \tan (70^{o}) \frac{\sin (70^{o})}{\cos (70^{o})} - \frac{\sin (70^{o})}{\cos (70^{o})} = 0$

03

Conclusion

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

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Most popular questions from this chapter

A function for which $f (x) = f (- x)$ for all $x$ in the domain of $f$ is called a(n) ___ function.

In Problem $85 a n d 86$ graph each of the function

$g (x) = \{\begin{cases} 2 \sin x i f 0 鈮� x 鈮� 蟺 \\ \cos x + 1 i f 蟺 < x 鈮� 2 蟺 \end{cases}$

Use a calculator to find the approximate value of each expression rounded to two decimal places.

$\cos 14 掳$

Find the amplitude, period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods.

$y = 2 \cos (3 x + \frac{蟺}{2})$

Convert each angle in degrees to radians. Express your answer as a multiple of $蟺$ .

$- 90 掳$

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