Question

solve 2cosx = -1 for 0<= x <=360

Answer 1

\[2cosx=-1\]
\[\frac{ 2cosx }{ 2 }=\frac{ -1 }{ 2 }\]
\[cosx=\frac{ -1 }{ 2 }\]

Now look at the unit circle
http://www.sciencedigest.org/UnitCircle.gif
When is the x-coordinate of a point on the circle -1/2?

Answer 2

cosine(x) is usually written cos(theta) because you have

Answer 3

you start at the x-axis (at 0 degrees or 0 radians) and go up to a certain point...this
point you may connect to the origin and this creates an angle with the x-axis

Answer 4

as you can see it may look like you have two answers....120 degrees in radians it's 2pi/3 and 240 degrees in radians 4pi/3
but check this out
you may also solve your equation using the inverse of cosine (or arccosine)
so you have
x=arccos(-1/2) and your calculator will probably give you 120 degrees