Find all solutions 1) 6costheta=-3

Question

im very confused with trigonometry i need help with this question

Answer 1

6Cos(θ)=-.5 ,  Cos(θ)=-.5/6 ,   Cos(θ)=-.5/6=-.08333 , taking the arc cos gives Θ=94.78 deg and θ=265.2 deg.

 

Cos(θ) is side adjacent/hypotenuse. Since it is a negative, the angle must be in the 2nd or 3rd quadrant. That is why there are 2 possible answers. Unless specified I would use the 1st answer Θ=94.78 deg

Answer 2

Dividing by 6, we have cos θ = -½

 

since this is negative, we know that the angle must be in quadrants II or III.  Making a suitable drawing is helpful.

 

The reference triangle has horizontal leg ½ and so the reference angle must be 60^o

 

therefore the solutions are 180^o±60^o or the same with any multiple of 360^o