Domanda del libro di testo
Find the length to three significant digits of each arc intercepted by a central angle in a circle of radius r. See Example 1. r = 12.3 cm , θ = 2π/3 radians
542
views
Ch. 3 - Radian Measure and The Unit Circle
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 4, Problema 13
Use the formula ω = θ/t to find the value of the missing variable.
ω = 0.91 radian per min, t = 8.1 min
Guida verificata passo dopo passo1
Identify the given variables and the formula: angular velocity \(\omega = 0.91\) rad/min, time \(t = 8.1\) min, and the formula \(\omega = \frac{\theta}{t}\) where \(\theta\) is the angular displacement in radians.
Rearrange the formula to solve for the missing variable \(\theta\): multiply both sides of the equation by \(t\) to get \(\theta = \omega \times t\).
Substitute the known values into the rearranged formula: \(\theta = 0.91 \times 8.1\).
Perform the multiplication to find the angular displacement \(\theta\) in radians (do not calculate the final value here, just set up the expression).
Interpret the result as the total angle in radians that the object has rotated through in the given time.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Concetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Angular Velocity (ω)
Angular velocity measures how fast an object rotates or revolves, expressed in radians per unit time. It indicates the angle covered per unit time, such as radians per minute, and is a fundamental quantity in rotational motion.
Video consigliato:
Percorso guidato
03:48
Introduction to Vectors
Angular Displacement (θ)
Angular displacement is the angle through which an object has rotated, measured in radians. It represents the change in the angular position of the object and is the product of angular velocity and time when motion is uniform.
Relationship Between Angular Velocity, Displacement, and Time
The formula ω = θ / t relates angular velocity (ω), angular displacement (θ), and time (t). Given any two variables, the third can be found by rearranging the formula, making it essential for solving problems involving rotational motion.
Video consigliato:
Percorso guidato
6:50Convert Equations from Polar to Rectangular
Pratica correlata
Domanda del libro di testo
Find the exact values of (a) sin s, (b) cos s, and (c) tan s for each real number s. See Example 1.
s = ―π
915
views
Domanda del libro di testo
Convert each radian measure to degrees.
8π/3
718
views
Domanda del libro di testo
Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 30°
609
views
Domanda del libro di testo
Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 90°
621
views
Domanda del libro di testo
Find the exact values of (a) sin s, (b) cos s, and (c) tan s for each real number s. See Example 1.
s = 2π
732
views