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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.94 (page 396)

Find the exact value of $\cos (1^{0}) + \cos (2^{o}) + \cos (3^{o}) + . . . . . + \cos (359^{o})$

Short Answer

Expert verified

The exact value of $\cos (1^{0}) + \cos (2^{o}) + \cos (3^{o}) + . . . . . + \cos (359^{o}) i s - 1$

Step by step solution

01

Step !: Given information

We are given a equation $\cos (1^{0}) + \cos (2^{o}) + \cos (3^{o}) + . . . . . + \cos (359^{o})$

02

Use the periodicity of the cosine function cos180-θ=-cosθcos360-θ=cosθ

We get

$\cos (1^{0}) + \cos (2^{o}) + \cos (3^{o}) + . . . + \cos (358^{o}) + \cos (359^{o}) + \cos (360^{o}) = 0 - 1 = - 1$

03

Conclusion

The value of $\cos (1^{0}) + \cos (2^{o}) + \cos (3^{o}) + . . . + \cos (360^{o}) i s - 1$

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Most popular questions from this chapter

In problems 13-20, $P (x, y)$ is the point on the unit circle that corresponds to a real number $t$ . Find the exact values of the six trigonometric functions of $t$ .

$(- \frac{1}{5}, \frac{2 \sqrt{6}}{5})$ .

In Problems 13鈥�20, $P (x, y)$ is the point on the unit circle that corresponds to a real number $t$ . Find the exact values of the six trigonometric functions of $t$ .

$(- \frac{2}{5}, \frac{\sqrt{21}}{5})$ .

In Problems $1 - 3$ , convert each angle in degrees to radians. Express your answer as a multiple of $蟺$ .

$3 . 13 掳$

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$\frac{13 蟺}{6}$

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