Skip to main content
Ch. 1 - Trigonometric Functions
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. 1 - Trigonometric FunctionsProblema 119
Capitolo 2, Problema 119

Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. 90 °

Guida verificata passo dopo passo
1
Start by sketching the angle of 90° in standard position. This means drawing the initial side along the positive x-axis and rotating the terminal side 90° counterclockwise, which will point straight up along the positive y-axis.
Draw an arrow from the initial side to the terminal side to represent the 90° rotation in the counterclockwise direction, indicating a positive angle.
To find a positive coterminal angle, add 360° to 90°, using the formula \(\theta_{coterminal} = \theta + 360k\), where \(k\) is an integer. For \(k=1\), the positive coterminal angle is \(90° + 360° = 450°\).
To find a negative coterminal angle, subtract 360° from 90°, again using \(\theta_{coterminal} = \theta + 360k\). For \(k=-1\), the negative coterminal angle is \(90° - 360° = -270°\).
Determine the quadrant for each angle: 90° lies on the positive y-axis (between Quadrant I and II), 450° is equivalent to 90° and also lies on the positive y-axis, and -270° also ends at the same position on the positive y-axis. Since these angles lie exactly on the axis, they are not in any quadrant but on the boundary between Quadrants I and II.

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:
2m

Concetti chiave

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

Standard Position of an Angle

An angle is in standard position when its vertex is at the origin of the coordinate plane and its initial side lies along the positive x-axis. The angle is measured by rotating the initial side to the terminal side, either counterclockwise for positive angles or clockwise for negative angles.
Video consigliato:
Percorso guidato
05:50
Drawing Angles in Standard Position

Coterminal Angles

Coterminal angles share the same terminal side but differ by full rotations of 360°. To find coterminal angles, add or subtract multiples of 360° from the given angle. For example, angles of 90°, 450°, and -270° are coterminal.
Video consigliato:
Percorso guidato
04:46
Coterminal Angles

Quadrants of the Coordinate Plane

The coordinate plane is divided into four quadrants numbered counterclockwise starting from the upper right. The quadrant of an angle depends on the location of its terminal side: 90° lies on the positive y-axis, between Quadrants I and II, so it is not strictly in any quadrant but on the boundary.
Video consigliato:
Percorso guidato
6:36
Quadratic Formula
Pratica correlata
Domanda del libro di testo

Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. 174 °

701
views
Domanda del libro di testo

Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. ―61 °

632
views
Domanda del libro di testo

Solve each problem. See Example 6. Revolutions of a Turntable A turntable in a shop makes 45 revolutions per min. How many revolutions does it make per second?

657
views
Domanda del libro di testo

Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. ―90 °

573
views
Domanda del libro di testo

Solve each problem. See Example 6. Rotating Airplane Propeller An airplane propeller rotates 1000 times per min. Find the number of degrees that a point on the edge of the propeller will rotate in 2 sec.

676
views
Domanda del libro di testo

Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. 300 °

717
views