Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 4 - Section 4.4 - Trigonometric Functions of Any Angle - Exercise Set - Page 575: 61


$\cos 225^{\circ}= -\dfrac{\sqrt 2}{2}$

Work Step by Step

The reference angle of an angle $0 \leq \theta \lt 2\pi $ based on its position can be computed by using the following steps: a) Quadrant- I: $\theta $ b) Quadrant- II: $180^{\circ}-\theta $ c) Quadrant -III: $\theta - 180^o $ d) Quadrant -IV: $360^{\circ}-\theta $ We can see that the angle $225^{\circ}$ lies in Quadrant III. Therefore, we have : Reference angle of $225^{\circ}$ is equal to $ =225^{\circ}-180^{\circ}=45^{\circ}$ Since, $\cos 45^{\circ}=\dfrac{\sqrt 2}{2}$ So, $\cos 225^{\circ}= -\dfrac{\sqrt 2}{2}$; Because $\theta $ lies in Quadrant-III.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.