Algebra and Trigonometry 10th Edition

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

Chapter 7 - Review Exercises - Page 552: 48


$sin~375°=\frac{\sqrt 6-\sqrt 2}{4}$ $cos~375°=\frac{\sqrt 6+\sqrt 2}{4}$ $tan~375°=\frac{\sqrt 3-1}{\sqrt 3+1}$

Work Step by Step

$sin~375°=sin~(135°+240°)=sin~135°~cos~240°+cos~135°~sin~240°=\frac{\sqrt 2}{2}(-\frac{1}{2})+(-\frac{\sqrt 2}{2})(-\frac{\sqrt 3}{2})=-\frac{\sqrt 2}{4}+\frac{\sqrt 6}{4}=\frac{\sqrt 6-\sqrt 2}{4}$ $cos~375°=cos~(135°+240°)=cos~135°~cos~240°-sin~135°~sin~240°=-\frac{\sqrt 2}{2}(-\frac{1}{2})-\frac{\sqrt 2}{2}(-\frac{\sqrt 3}{2})=+\frac{\sqrt 2}{4}+\frac{\sqrt 6}{4}=\frac{\sqrt 6+\sqrt 2}{4}$ $tan~375°=tan(135°+240°)=\frac{tan~135°+tan~240°}{1-tan~135°~tan~240°}=\frac{-1+\sqrt 3}{1-(-1)\sqrt 3}=\frac{\sqrt 3-1}{\sqrt 3+1}$
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