Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 7 - 7.5 - Multiple-Angle and Product-to-Sum Formulas - 7.5 Exercises - Page 548: 35


$sin~75°=\frac{\sqrt {2+\sqrt 3}}{2}$

Work Step by Step

$75°$ lies in the first quadrant. So, $sin~75°\gt0$: $sin~75°=sin\frac{150°}{2}=+\sqrt {\frac{1-cos~150°}{2}}=\sqrt {\frac{1-(-\frac{\sqrt 3}{2})}{2}}=\sqrt {\frac{2+\sqrt 3}{4}}=\frac{\sqrt {2+\sqrt 3}}{2}$
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