In the standard (x,y) coordinate plane below, an angle is shown whose vertex is the origin

In the standard (x,y) coordinate plane below, an angle is shown whose vertex is the origin. One side of this angle with measure θ passes through (4,-3), and the other side includes the positive x-axis. What is the cosine of θ ?

  1. -4/3
  2. -3/4
  3. -3/5
  4. 4/5
  5. 5/4

Answer

The correct answer is D.

The figure shows the 3-4-5 right triangle with sides formed by the x-axis, the vertical line through (4,-3), and the terminal side of θ.

The angle, α, formed by the terminal side and the x-axis is called the reference angle of θ.

cos α = 4/5

As the terminal side of θ lies in Quadrant IV, cos θ is positive. Therefore, cos θ = 4/5.