Answer:
210 is the only choice I see listed that works.
Step-by-step explanation:
I don't know if you know this but you can apply a co-function identity here giving you the equation:
[tex]cos(x)=-\frac{\sqrt{3}}{2}[/tex].
If you are unsure of the identity sin(90-x)=cos(x) then I can show you another identity that leads to this one.
The difference identity for sine is sin(a-b)=sin(a)cos(b)-sin(b)cos(a).
Applying this to sin(90-x) gives you sin(90)cos(x)-sin(x)cos(90).
Let's simplify that using that sin(90)=1 while cos(90)=0:
sin(90-x)=sin(90)cos(x)-sin(x)cos(90)
sin(90-x)=1cos(x)-sin(x)(0)
sin(90-x)=cos(x)
You can also prove this identity using a right triangle like the one in this picture:
That missing angle is 90-x since we need the angles in this triangle to add up to 180 which it does:
(x)+(90)+(90-x)
x+90+90-x
x-x+90+90
0+180
180
Anyways you should see that sin(90-x)=b/c while cos(x)=b/c.
Since they are equal to the same ratio, then you can say sin(90-x)=cos(x).
There are other co-function identities you can get from using this idea.
Anyways back to the problem.
We are solving:
[tex]cos(x)=-\frac{\sqrt{3}}{2}[/tex].
It looks like you have a drop-down menu with answers ranging from 0 to 360.
So I'm going to answer in degrees using the unit circle.
cosine value refers to the x-coordinate.
We are looking for when the x-coordinate is [tex]-\frac{\sqrt{3}}{2}[/tex] which is at [tex]\theta=150^\circ , 210^\circ[/tex].
