Question #c88fc

1 Answer
Apr 26, 2017

50.1^o, 154.3^o, 205.7^o, 309.0^o

Explanation:

Start by completing the square as this expression cannot be factorised.

3cos^2x+cosx-1=0

cos^2x+1/3cosx-1/3=0

(cosx-1/6)^2-1/36-1/3=0

(cosx-1/6)^2 = 13/36

cosx-1/6 = +-sqrt(13/36)

cosx=1/6 +-sqrt(13)/6

cosx=1/6(1 +-sqrt(13))

Now we look at a graph to see where the solutions will lie.

Geogebra

The graph shows solutions in radians. Solutions in degrees are as follows

50.1^o, 154.3^o, 205.7^o, 309.0^o