Question #c88fc

Question

923 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-26T17:05:36

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

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

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