Answered: If the given angle is in standard…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.3: The Addition And Subtraction Formulas

Problem 15E

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Question

If the given angle is in standard position, find one positive and one negative co-terminal angle for each: (a) 5π 3 (b) −132◦

Expert Solution

Step 1

It is known that, Co-terminal angles: are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side.

(a)

Obtain the negative co-terminal angle for $\frac{5 π}{3}$ .

$\begin{array}{rcl} \frac{5 π}{3} + x & = & 2 π \\ x & = & 2 π - \frac{5 π}{3} \\ = & \frac{π}{3} (N e g a t i v e d i r e c t i o n) \\ = & - \frac{π}{3} \end{array}$

Therefore, the negative co-terminal angle for $\frac{5 π}{3}$ is $- \frac{π}{3}$ .

Obtain the positive co-terminal angle for $\frac{5 π}{3}$ .

$\begin{array}{rcl} x & = & 2 π + \frac{5 π}{3} \\ = & \frac{11 π}{3} \end{array}$

Therefore, the positive co-terminal angle for $\frac{5 π}{3}$ is $\frac{11 π}{3}$ .

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