If angle θ is in standard position and intersects the unit circle at find and .
B)
C)
D)

Question

If angle θ  is in standard position and intersects the unit circle at   find   and  . ​
B)​ 
C)​ 
D)​

Quizplus · Accepted Answer

To find the coordinates of the point of intersection, we use the unit circle, where the equation is $$x^2 + y^2 = 1$$
Since $	heta$ intersects the x-axis at $(1, 0)$, its coordinates are $(\cos	heta, \sin	heta) = (1,0)$.
Therefore, $\cos	heta = 1$ and $\sin	heta = 0$. This means that the terminal side of $	heta$ lies on the positive x-axis.
Since the unit circle is a circle of radius 1 centered at the origin, the coordinates of the point of intersection are $(\cos	heta, \sin	heta) = (1, 0)$.
To find the values of $\sin(2	heta)$ and $\cos(2	heta)$, we use double angle identities.
$$\cos(2	heta) = \cos^2	heta - \sin^2	heta = 1^2 - 0^2 = 1$$
$$\sin(2	heta) = 2\sin	heta\cos	heta = 2(0)(1) = 0$$
Therefore, the answer is (B).

If Angle θ Is in Standard Position and Intersects the Unit