Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 1 - Section 1.3 - Definition I: Trigonometric Functions - 1.3 Problem Set - Page 32: 23

Answer

Sinex=$\frac{\sqrt 2}{2}$ Cosx=$-\frac{\sqrt 2}{2}$ Tanx=$-1$ Point on terminal angle:-(1,1)

Work Step by Step

The reference angle for $135^{\circ}$ is $45^{\circ}$. According to our unit circle, the sine of $45^{\circ}$ is $\frac{\sqrt 2}{2}$. Since the angle 135 is in the second quadrant, it is positive, which gives us $\frac{\sqrt 2}{2}$. The cos of our reference angle is $\frac{\sqrt 2}{2}$ as well, but cosine is negative in the second quadrant, so we have$-\frac{\sqrt 2}{2}$. The tangent of our reference angle is 1, but tangent is negative in the second quadrant, which gives us -1. The terminal side of the angle will intersect the point (-1,1). Sinex=$\frac{\sqrt 2}{2}$ Cosx=$-\frac{\sqrt 2}{2}$ Tanx=$-1$ Point on terminal angle:-(1,1)
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