Solve the equation on the interval 0 less than or equals theta less than 2 pi 0≤θ<2π. 2 cosine theta plus 1 equals 0 2cosθ+1=0

Question

Solve the equation on the interval
0 less than or equals theta less than 2 pi
0≤θ<2π.

2 cosine theta plus 1 equals 0
2cosθ+1=0

Answer 1

Hi Alexandra

 

What we need to do is to isolate the "cosθ" term.

 

So subtract 1 from both sides.

2cosθ=-1

 

Then divide both sides by 2

cosΘ=-(1/2)

 

Now figure out what angles (Θ) have a cosine of (-1/2).

 

Cosine corresponds to the x-coordinate,  Sine corresponds to the y-coordinate.

 

SO if the cosine is negative, that means that the triangles are to the left of the y-axis.

 

(I wish I could draw it for you....)

 

One triangle extends from the origin into the 2nd Quadrant at a 60 degree reference angle.

The other triangle extends from the origin into the 3rd Quadrant at a 60 degree reference angle.

 

These two angles in standard position are (2π/3) and (4π/3).