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Ch. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric Functions
Blitzer - Trigonometry 3rd Edition
Blitzer3rd EditionTrigonometryISBN: 9780137316601Not the one you use?Change textbook
All textbooksBlitzer 3rd EditionCh. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric FunctionsProblem 61
Chapter 2, Problem 61

In Exercises 61–62, use the figures shown to find the bearing from O to A.
Diagram showing angle 61° from point O to point S in a coordinate system.

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Identify the reference direction for bearings, which is always measured clockwise from the north line.
Observe that the vector OS makes a 61° angle with the east direction, measured counterclockwise from the east axis to the vector OS.
Since bearings are measured clockwise from north, calculate the bearing by starting at north (0°) and moving clockwise to the vector OS.
Note that the angle between north and east is 90°, so the bearing from north to the vector OS is 90° minus the given 61° angle.
Express the bearing from point O to point S as \(90^\circ - 61^\circ\) to find the final bearing in degrees.

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Key Concepts

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

Bearing and Compass Directions

Bearing is a way to describe direction using degrees measured clockwise from the north line. It is commonly used in navigation and surveying to specify the direction from one point to another relative to the north.
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Angle Measurement and Reference Lines

Angles in navigation are measured from a reference direction, usually north, moving clockwise. Understanding how to interpret angles relative to compass directions is essential for converting given angles into bearings.
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Coordinate System and Quadrants

The coordinate system with north, south, east, and west axes helps visualize directions and angles. Recognizing the quadrant in which a vector lies aids in correctly determining the bearing by relating the angle to the compass points.
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