Question

Please help ASAP!! Thank youu

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 60° 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: Find the angle represented by the lighthouse on the unit circle.

On the unit circle, the angle represented by the lighthouse would be 60°.

Part 2: Determine the exact ordered pair associated with the lighthouse on the unit circle.

To find the exact ordered pair associated with the lighthouse on the unit circle, we need to use the formula:

(cos(angle), sin(angle))

Plugging in the angle of 60°, we get:

(cos(60°), sin(60°))

This simplifies to:

(0.5, √3/2)

So the exact ordered pair associated with the lighthouse on the unit circle is (0.5, √3/2).

Part 3: Find the exact sine, cosine, and tangent of the angle on the unit circle.

The sine of the angle on the unit circle is sin(60°) = √3/2

The cosine of the angle on the unit circle is cos(60°) = 0.5

The tangent of the angle on the unit circle is tan(60°) = √3/0.5 = √3/2

So the exact sine, cosine, and tangent of the angle on the unit circle are √3/2, 0.5, and √3/2, respectively.

Answer 2

Explanation:

Part 1: Find the angle represented by the lighthouse on the unit circle.

The bearing of the lighthouse is measured clockwise from due north, so the angle represented by the lighthouse on the unit circle is equal to the bearing. In this case, the angle is 60°.

Part 2: Determine the exact ordered pair associated with the lighthouse on the unit circle.

To find the exact ordered pair associated with the lighthouse on the unit circle, we need to use the angle that we found in part 1 and the definition of the unit circle.

The unit circle is a circle with radius 1 centered at the origin of a coordinate plane. The coordinates of a point on the unit circle can be determined by taking the angle formed by the point and the positive x-axis and using it to find the x- and y-coordinates of the point.

In this case, the angle formed by the lighthouse and the positive x-axis is 60°. Using the definition of the unit circle, we can find the x-coordinate by taking the cosine of the angle, and the y-coordinate by taking the sine of the angle.

The cosine of 60° is 0.5, and the sine of 60° is √3 / 2. Therefore, the exact ordered pair associated with the lighthouse on the unit circle is (0.5, √3 / 2).

Part 3: Find the exact sine, cosine, and tangent of the angle on the unit circle.

The sine, cosine, and tangent of an angle on the unit circle are defined as the y-coordinate, x-coordinate, and y-coordinate divided by the x-coordinate, respectively, of the point on the unit circle that is associated with the angle.

In this case, we have already found that the sine of the angle is √3 / 2 and the cosine of the angle is 0.5. Therefore, we can find the tangent of the angle by dividing the sine by the cosine: (√3 / 2) / 0.5 = √3.

Therefore, the exact sine, cosine, and tangent of the angle on the unit circle are √3 / 2, 0.5, and √3, respectively.