A unit circle is simply a circle that has a radius of 1.
The measure of the angle is 180 degrees.
The domain is given as:
[tex]\mathbf{0 \le \theta \le 360}[/tex]
The point is given as:
[tex]\mathbf{P = (-1,0)}[/tex]
A point is represented as:
[tex]\mathbf{(\cos(\theta),\sin(\theta)) = (x,y)}[/tex]
So, we have:
[tex]\mathbf{(\cos(\theta),\sin(\theta)) = (-1,0)}[/tex]
By comparison, we have:
[tex]\mathbf{\cos(\theta) = -1}[/tex]
[tex]\mathbf{\sin(\theta) = 0}[/tex]
Calculate tangent
[tex]\mathbf{\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}}[/tex]
[tex]\mathbf{\tan(\theta) = \frac{0}{-1}}[/tex]
[tex]\mathbf{\tan(\theta) = 0}[/tex]
The above values means that the angle is on the quadrant.
So, the possible values are:
[tex]\mathbf{\theta = 90, 180, 270,360}[/tex]
Because cosine is negative, the angle becomes
[tex]\mathbf{\theta =180}[/tex]
Hence, the measure of the angle is 180 degrees.
Read more about unit circles at:
https://brainly.com/question/22380956
