Use inverse trigonometric functions to find the solutions of the equation that are in the given interval, and approximate the solutions to four decimal places.

Question

Use inverse trigonometric functions to find the solutions of the equation that are in the given interval, and approximate the solutions to four decimal places. (Enter your answers as a comma-separated list.)

(cos x)(8 cos x + 2) = 3;     [0, 2𝜋)

Answer 1

cosx(8cosx +2) = 3

8cos^2(x) + 2cosx -3 = 0

factor

(4cosx +3)(2cosx -1)= 0

set each factor = 0 and solve for x

cosx = 1/2

x = pi/3 =60 degrees and 5pi/3 = 300 degrees

x = pi/3, 5pi/3 or 60, 300 degrees

4cosx=-3

cosx =-3/4

x = arccos(-3/4) =138.5904, 360-138.5904 = 221.4096 degrees

or 138.5904pi/180, 221.4096pi/180

= about .7699pi, 1.2301pi

x= pi/3, 5pi/3, .7699pi, 1.2301pi

or

x= 60, 138.5904, 221.4096, 300 degrees