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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.93 (page 396)

Find the exact value of $\sin (1^{o}) + \sin (2^{o}) + \sin (3^{o}) + . . . . + \sin (360^{o})$

Short Answer

Expert verified

The exact value of $\sin (1^{o}) + \sin (2^{o}) + . . . . + \sin (360^{o})$ is $0$

Step by step solution

01

given information

We are given $\sin (1^{o}) + \sin (2^{o}) + . . . . + \sin (360^{o})$

02

Use periodicity propertysinθ=sinθ-2π

We get

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

03

Conclusion

The exact value of $\sin (1^{o}) + \sin (2^{o}) + . . . . + \sin (360^{o}) i s 0 .$

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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 $t$ .

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