Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

2. Trigonometric Functions on Right Triangles

Trigonometric Functions on Right Triangles

Trigonometry

2. Trigonometric Functions on Right Triangles

Trigonometric Functions on Right Triangles

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2:13 minutes

Problem 61

Textbook Question

In Exercises 61–62, use the figures shown to find the bearing from O to A.

Verified step by step guidance

Identify the direction of the bearing from point O to point A, which is indicated by the arrow in the diagram.

Notice that the angle given is 61° from the North direction towards the East direction.

Understand that bearings are typically measured clockwise from the North direction.

Calculate the bearing by adding the given angle (61°) to the standard North direction (0°).

Express the final bearing as a three-digit number, which is the sum of 0° and 61° in this case.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Bearing

Bearing is a way of describing direction in navigation and geometry, typically expressed in degrees. It is measured clockwise from the north direction, with 0° representing north, 90° east, 180° south, and 270° west. Understanding how to calculate bearings is essential for determining the direction from one point to another, as seen in the question.

Angles in Standard Position

An angle is in standard position when its vertex is at the origin of a coordinate system and its initial side lies along the positive x-axis. The angle is measured counterclockwise from the initial side. In this context, the 61° angle from point O to point S indicates the direction of point S relative to the north, which is crucial for calculating the bearing.

Trigonometric Functions

Trigonometric functions, such as sine, cosine, and tangent, relate the angles of a triangle to the lengths of its sides. These functions are fundamental in solving problems involving angles and distances in trigonometry. In this question, they may be used to find the coordinates of point A based on the angle and distance from point O, aiding in determining the bearing.