Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 2 - Acute Angles and Right Triangles - Section 2.1 Trigonometric Functions of Acute Angles - 2.1 Exercises - Page 54: 60


$sin (45^{\circ}) = \frac{1}{\sqrt{2}}$

Work Step by Step

Let's consider a triangle with angles $45^{\circ}, 45^{\circ},$ and $90^{\circ}$ that has sides of length $1, 1,$ and $\sqrt{2}$. Let $x = 1, y= 1$, and $r = \sqrt{2}$. Then: $sin(45^{\circ}) = \frac{y}{r} = \frac{1}{\sqrt{2}}$
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