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: 19


The solution set is $\{\varnothing\}$

Work Step by Step

$$\tan^2x+3=0$$ over interval $[0,2\pi)$ 1) Consider the equation: $$\tan^2x+3=0$$ $$\tan^2x=-3$$ We know that $A^2\ge0$ for $\forall A\in R$. As a result, $\tan^2x\ge0$ for $\forall x\in [0,2\pi)$ Therefore, as $-3\lt0$, there are no values of $x\in[0,2\pi)$ that $\tan^2x=-3$ In other words, the solution set of this equation is $\{\varnothing\}$
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