Answer
$ \frac{\sqrt 2+\sqrt 6}{4}$
Work Step by Step
$sin105^\circ=sin(150^\circ-45^\circ)=sin150^\circ cos45^\circ-cos150^\circ sin45^\circ=(\frac{1}{2})(\frac{\sqrt 2}{2})-(-\frac{\sqrt 3}{2})(\frac{\sqrt 2}{2})=\frac{\sqrt 2+\sqrt 6}{4}$
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 6 - Analytic Trigonometry - Section 6.5 Sum and Difference Formulas - 6.5 Assess Your Understanding - Page 508: 16
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