Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.1 Inverse Circular Functions - 6.1 Exercises - Page 260: 96

Answer

$0.9682458366$

Work Step by Step

To find $\sin(\cos^{-1} 0.25)$, we first need to find $\cos^{-1} 0.25$. Ensuring that the calculator is in radians, we type $\cos^{-1} 0.25$ into the calculator and solve: $\cos^{-1} 0.25\approx1.318116072$ $\sin(\cos^{-1} 0.25)$ now becomes $\sin (1.318116072)$. Typing $\sin (1.318116072)$ into the calculator and solving: $\sin (1.318116072)\approx0.9682458366$ Therefore, $\cos(\tan^{-1} 0.5)\approx0.9682458366$
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