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)(14 cos x + 1) = 4;     [0, 2𝜋)



Answer 1

First multiply this out to get 14cos^2(x)+cos(x)=4

14cos^2(x) +cos(x) -4= 0 This can be factored ( use factoring by grouping) to

(7cos(x) +4)( 2cos(x)-1)= 0 so

7 cos(x)= -4

cos(x)= -4/7 take inverse cosine and you get x= 2.1790 radians and x = -2.179 radians

2cos(x) -1= 0

2cos(x)= 1

cos(x) = 1/2 x= pi/3 and 5pi/3 so your 4 solutions are

( pi/3, 5pi/3. 2.1790 radians and -2.179radians)