Precalculus question

Question

Find all solutions to the following equation on the interval [0,pi) without the use of a graphing utility:

3cos⁡(t)+4=2.

If there are more than one solution, separate them with spaces. If there is no solution, write "NA".

Solve algebraically, showing all steps that lead to your response. 

Answer 1

3cost +4 = 2

3 cost = 2-4 =-2

cost=-2/3= about -.667

negative means 2nd or 3rd quadrant

near -sqr2/2= -.707 means close to 5pi/4 or 135 degrees

and close to 5pi/4 or 225 degrees'

use a calculator with an inverse trig function

t = cos^(-2/3) =about 131.81 degrees and 228.19 degrees

or equivalent in radians

Answer 2

3 cos t + 4 = 2

3 cos t = -2

cos t = -2/3

cos^-1 (-2/3) = t

2.30 = t