Question

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

The image shows a unit circle and a right triangle in quadrant 1 with a 60-degree angle in standard position. The hypotenuse, which is also the terminal side of the angle, has a length of 1. The terminal side intersects the circle at (one half, the square root of 3 over 2).

Answer 1

For the 60° angle in standard position on the unit circle the terminal point is (cos 60°, sin 60°) = (1/2, √3/2).

Thus the exact trigonometric values are:
- cos 60° = 1/2
- sin 60° = √3/2
- tan 60° = sin/cos = √3
- sec 60° = 1/cos = 2
- csc 60° = 1/sin = 2/√3 = 2√3/3
- cot 60° = 1/tan = 1/√3 = √3/3

(These come from the right triangle with hypotenuse 1, adjacent 1/2 and opposite √3/2.)