An equation is given Enter your answers as a commaseparated

An equation is given. (Enter your answers as a comma-separated list. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)

(a) 2 cos 3 = 1

Find all solutions of the equation.

theta=

(b) Find the solutions in the interval [0,2pi)

theta=

Solution

a)   2 cos 3 theta = 1

dividing the entire equation by 2

cos 3 theta = 1/2

therefore,

3 theta = pi/3 + 2pin , theta = ( pi + 6pi*n ) / 9

3 theta = 5pi/3 + 2pin , theta = ( 5pi + 6 pi*n ) / 9

general solutions are :

theta = ( pi + 6pi*n ) / 9 , ( 5pi + 6 pi*n ) / 9

b) solutions for the interval [ 0,2pi )

theta = pi/9 , 17pi/9 , 11pi/9 , 13pi/9 , 5pi/9 , 7pi/9