Find all radian solutions to the following equation. (Give all answers as exact values in radians. Let k be any integer. Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)co(A - ) = -A =rad

The given equation is: cosA-π9=-12 Since, cos2π3=-12 Therefore, cosA-π9=cos2π3.

Answered: Find all radian solutions to the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section: Chapter Questions

Problem 28T

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Find all radian solutions to the following equation. (Give all answers as exact values in radians. Let k be any integer. Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
co(A - ) = -
A =
rad

Expert Solution

Step 1

The given equation is:

$\cos (A - \frac{π}{9}) = - \frac{1}{2}$

Since,

$\cos (\frac{2 π}{3}) = - \frac{1}{2}$

Therefore, $\cos (A - \frac{π}{9}) = \cos (\frac{2 π}{3})$ .

Step 2

The general solution of $\cos (x) = \cos (α)$ is given by: $x = 2 k π \pm α$ , where k is an integer.

Thus, the general solution of the equation $\cos (A - \frac{π}{9}) = \cos (\frac{2 π}{3})$ is

$A - \frac{π}{9} = 2 k π \pm (\frac{2 π}{3}) A = 2 k π \pm (\frac{2 π}{3}) - \frac{π}{9}$

$A = 2 k π + (\frac{2 π}{3}) - \frac{π}{9}, 2 k π - (\frac{2 π}{3}) - \frac{π}{9} A = 2 k π + \frac{2 π}{3} - \frac{π}{9}, 2 k π - \frac{2 π}{3} - \frac{π}{9} A = 2 k π + \frac{5 π}{9}, 2 k π - \frac{7 π}{9} rad$

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