Question

Navigators locate an object by measuring its location clockwise direction from due north. The measure of the angle is called the bearing.

Suppose a lighthouse's bearing is 150° from an island.
Be sure to show and explain all work for each part.

Part 1: Find the angle represented by the lighthouse on the unit circle.
Part 2: Determine the exact ordered pair associated with the lighthouse on the unit circle.
Part 3: Find the exact sine, cosine, and tangent of the angle on the unit circle.

Answer 1

Part 1:

The bearing of the lighthouse is 150° from the island. This means that the lighthouse is located 150° clockwise from due north. On the unit circle, the angle 150° is represented by the point (-√3/2, -1/2).

Part 2:

The ordered pair associated with the lighthouse on the unit circle is (-√3/2, -1/2).

Part 3:

The sine of the angle 150° is -√3/2. The cosine of the angle 150° is -1/2. The tangent of the angle 150° is -√3.