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: 37


$sin~112°~30'=\frac{\sqrt {2+\sqrt 2}}{2}$ $cos~112°~30'=-\frac{\sqrt {2-\sqrt 2}}{2}$ $tan~112°~30'=-(1+\sqrt 2)$

Work Step by Step

$112°~30'$ lies in the second quadrant. $sin~112°~30'=sin\frac{225°}{2}=+\sqrt {\frac{1-cos~225°}{2}}=\sqrt {\frac{1-(-\frac{\sqrt 2}{2})}{2}}=\sqrt {\frac{2+\sqrt 2}{4}}=\frac{\sqrt {2+\sqrt 2}}{2}$ $cos~112°~30'=cos\frac{225°}{2}=-\sqrt {\frac{1+cos~225°}{2}}=-\sqrt {\frac{1-\frac{\sqrt 2}{2}}{2}}=-\sqrt {\frac{2-\sqrt 2}{4}}=-\frac{\sqrt {2-\sqrt 2}}{2}$ $tan~112°~30'=tan\frac{225°}{2}=\frac{1-cos~225°}{sin~225°}=\frac{1-(-\frac{\sqrt 2}{2})}{-\frac{\sqrt 2}{2}}=\frac{2+\sqrt 2}{-\sqrt 2}=-\sqrt 2-1=-(1+\sqrt 2)$
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