Answer
$\dfrac{\sqrt{2}}{2}$
Work Step by Step
$\because \sin{(\theta+ 360^{\circ} k)} = \sin{\theta}$
$\therefore \sin{405^{\circ}} = \sin{(45^{\circ}+360^{\circ})} = \sin{45^{\circ}}$
$\sin{45^{\circ}} = \boxed{\dfrac{\sqrt{2}}{2}}$
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 5.3 Properties of the Trigonometric Functions - 5.3 Assess Your Understanding - Page 417: 11
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