What is the cosine of an angle,θ , in standard position if its terminal ray intersects the unit circle at (0.64, -0.766? In which quadrant does this point lie?

Question

A) cos (θ)= 0.64, quadrant 4

B) cos (θ)= -0.77, quadrant 2

C) cos (θ)= -0.77, quadrant 4

D) cos (θ)= 0.64, quadrant 2

Answer 1

A point on the unit circle has a projection on both the x and y axis.

The projection on the x-axis is the cosine and on the y-axis it is the sine.

So in your example, cos = 0.64.

The given point has x > 0 and y < 0.

That is the characteristic of quadrant 4.