The angle 60 is shown below in standard position, together with a unit circle.

Question

A circle with a radius of 1 is shown with its center located at the origin on a coordinate grid. The radius forms a terminal side that makes a 60-degree-angle with the positive x-axis. The terminal side intersects the circle at (one half, the square root of 3 over 2).

Use the coordinates of the point of intersection of the terminal side and the circle to compute sec 60.

a) 2
b) 1/2
c) sqrt 3/2
d) sqrt 3/4

Answer 1

To compute sec 60, we first need to find the x-coordinate of the point of intersection on the unit circle.

The x-coordinate can be found using the formula x = cos(theta), where theta is the angle formed by the terminal side and the positive x-axis (60 degrees in this case).

So, x = cos(60) = 1/2.

Next, the secant function is defined as sec(theta) = 1/cos(theta). Therefore, sec 60 = 1 / (1/2) = 2.

Therefore, the correct answer is:

a) 2