Question

in a unit circle, \\( \theta = 180 ^ { \circ } \\). what is the terminal point?

a \\( ( 0,1 ) \\)
b \\( ( 0, - 1 ) \\)
c \\( ( - 1,0 ) \\)
d \\( ( 1,0 ) \\)

Explanation:

Step1: Recall the formula for terminal point

For a unit circle, the terminal point \((x,y)\) for an angle \(\theta\) is given by \((x,y)=(\cos\theta,\sin\theta)\).

Step2: Calculate \(x = \cos\theta\)

Given \(\theta = 180^{\circ}\), then \(x=\cos(180^{\circ})=- 1\).

Step3: Calculate \(y=\sin\theta\)

Given \(\theta = 180^{\circ}\), then \(y = \sin(180^{\circ})=0\).

Answer:

C. \((-1,0)\)