Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.2 Trigonometric Equations I - 6.2 Exercises - Page 273: 47


The solution set is $$\{180^\circ+360^\circ n, n\in Z\}$$

Work Step by Step

$$\cos\theta+1=0$$ 1) Solve the equation over the interval $[0^\circ,360^\circ)$ $$\cos\theta+1=0$$ $$\cos\theta=-1$$ Look at the unit circle, we find that over the interval $[0^\circ, 360^\circ)$, there is only one value of $\theta$ which $\cos\theta=-1$, which is $\theta=180^\circ$. Therefore, $$\theta=\{180^\circ\}$$ 2) Solve the equation for all solutions To find all solutions, we add the integer multiples of the period of cosine function, which is $360^\circ$ to each solution found in step 1. In detail, there is one solution found in step 1, $180^\circ$, so it will be written as $\theta=180^\circ+360^\circ n (n\in Z)$. In other words, the solution set is $$\{180^\circ+360^\circ n, n\in Z\}$$
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