Answer
$0$
Work Step by Step
$sin45^\circ+sin135^\circ+sin225^\circ+sin315^\circ\\ =sin45^\circ+sin(180-45)^\circ+sin(180+45)^\circ+sin(360-45)^\circ\\ =sin45^\circ+sin45^\circ-sin45^\circ-sin45^\circ=0$
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 5 - Trigonometric Functions - Section 5.2 Trigonometric Functions: Unit Circle Approach - 5.2 Assess Your Understanding - Page 403: 85
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