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 in quadrant 2

B) cos(θ) =-0.77 in quadrant 2

C) cos(θ) =-0.77 in quadrant 4

D) cos(θ) =0.64 in quadrant 4

Answer 1

Since the point is on the unit circle, (0.64, -0.766) = (cosθ, sinθ). So, cosθ = 0.64. Since the x-coordinate is positive and the y-coordinate is negative, the point lies in Q IV.

Answer 2

In which quadrant is x positive and y negative?

Use Pythagoras to determine the value of r.

cos θ = x / r