Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 6 - Section 6.1 - Solving Trigonometric Equations - 6.1 Problem Set - Page 325: 3

Answer

reference... $0^{o}$ ... $360^{o}$ ... $360^{o}k$

Work Step by Step

A trigonometric equation has expressions involving trigonometric functions on either side of the equality sign. Using algebraic means and properties of the trigonometric functions, the goal is to isolate ONE trigonometric function on one side, and a number on the other. Then, we seek out angles, for which the equality stands. We first find the reference angle (usually in the first quadrant), and check, using symmetry, for other solutions in the interval $0 \leq \theta \leq 360^{o}.$ Finally, because of the periodic nature of trigonometric functions, to each solution we add multiples of $360^{o}$ (written as $360^{o}k)$, to represent all possible values. Answer: reference... $0^{o}$ ... $360^{o}$ ... $360^{o}k$
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