Trigonometry (11th Edition) Clone

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

Chapter 4 - Quiz (Sections 4.1-4.2) - Page 164: 10


$y= -\sin x$

Work Step by Step

Upon inspection, we find that the graph shows an inverted sin function with an amplitude of 1 and a period of $2\pi$. The standard equation $y=a \sin bx$ becomes $y=-a \sin bx$ if the graph is an inverted sin function. In the equation $y=-a \sin bx$, $a$ is the amplitude. Since the amplitude is 1, $a$ is equal to 1. To find the value of $b$, we use the formula: Step 1: Period$=\frac{2\pi}{b}$ Step 2: $2\pi=\frac{2\pi}{b}$ Step 3: $b=\frac{2\pi}{2\pi}$ Step 4: $b=1$ Substituting the values of $a$ and $b$ in the equation $y=-a \sin bx$, we find that the equation of the graph is $y= -\sin x$.
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