Ch. 2 - Acute Angles and Right Triangles

Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo

Lial 12th Edition

Ch. 2 - Acute Angles and Right Triangles

Problema 2.5.18

Capitolo 3, Problema 2.5.18

Concept Check The two methods of expressing bearing can be interpreted using a rectangular coordinate system. Suppose that an observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at each point. Express the bearing using both methods. (2, 2)

Guida verificata passo dopo passo

Identify the position of the airplane relative to the radar station at the origin. The coordinates given are (2, 2), which means the airplane is 2 units east and 2 units north of the radar station.

Calculate the angle \( \theta \) that the line from the origin to the point (2, 2) makes with the positive x-axis (east direction) using the tangent function: \( \tan(\theta) = \frac{y}{x} = \frac{2}{2} \).

Find \( \theta \) by taking the arctangent (inverse tangent) of \( \frac{2}{2} \), which gives the angle in degrees or radians measured counterclockwise from the positive x-axis.

Express the bearing in the first method (the compass bearing) by converting the angle \( \theta \) to a compass bearing, which is typically measured clockwise from the north (positive y-axis). Since \( \theta \) is measured from east, use the relationship: \( \text{bearing} = 90^\circ - \theta \).

Express the bearing in the second method (the azimuth bearing) as the angle \( \theta \) measured clockwise from the north direction, or equivalently, the angle from the positive y-axis to the point, which can be found by adjusting \( \theta \) accordingly.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Bearing and Its Methods

Bearing is a way to describe direction relative to a reference direction, usually north. The two common methods are the compass bearing, measured clockwise from north (0° to 360°), and the quadrant bearing, expressed as an angle east or west of north or south (e.g., N45°E). Understanding both methods is essential to convert and interpret directions accurately.

Video consigliato:

Percorso guidato

6:36

Quadratic Formula

Rectangular Coordinate System and Position Vectors

In a rectangular coordinate system, points are represented by (x, y) coordinates relative to the origin. The position vector from the origin to a point defines the direction and distance of the object. This system helps translate spatial locations into angles and distances, which are necessary for calculating bearings.

Video consigliato:

Percorso guidato

5:10

Introduction to Graphs & the Coordinate System

Calculating Angles Using Trigonometric Functions

To find the bearing from coordinates, use trigonometric functions like tangent to calculate the angle between the position vector and the reference axis (usually the positive y-axis for north). The arctangent function helps determine the angle from the x and y coordinates, which can then be converted into the appropriate bearing format.

Video consigliato:

Percorso guidato

4:45

How to Use a Calculator for Trig Functions

Pratica correlata

Domanda del libro di testo

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2. cot θ = 0.21563481

789

views

Domanda del libro di testo

Solve each problem. See Examples 1 and 2. Distance Traveled by a Ship A ship travels 55 km on a bearing of 27° and then travels on a bearing of 117° for 140 km. Find the distance from the starting point to the ending point.

940

views

Domanda del libro di testo

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1.

cos(90°-3.69°)

671

views

Domanda del libro di testo

Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. cos 70° = 2 cos² 35° - 1

556

views

Domanda del libro di testo

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2.

sin θ = 0.84802194

692

views

Domanda del libro di testo

Find two angles in the interval [0°, 360°) that satisfy each of the following. Round answers to the nearest degree. tan θ = 0.70020753

621

views