Domanda del libro di testo
The propeller of a 90-horsepower outboard motor at full throttle rotates at exactly 5000 revolutions per min. Find the angular speed of the propeller in radians per second.
789
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 3.5
Convert each degree measure to radians. Leave answers as multiples of π .
45°
Guida verificata passo dopo passo1
Recall the formula to convert degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
Substitute the given degree measure into the formula: \(45^\circ \times \frac{\pi}{180}\).
Simplify the fraction \(\frac{45}{180}\) by dividing numerator and denominator by their greatest common divisor.
Express the simplified fraction multiplied by \(\pi\) to write the answer as a multiple of \(\pi\).
Write the final answer in the form \(\frac{\text{numerator}}{\text{denominator}}\pi\) without calculating the decimal value.
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.
Degree to Radian Conversion
Degrees and radians are two units for measuring angles. To convert degrees to radians, multiply the degree measure by π/180. This conversion is essential because radians are the standard unit in many mathematical contexts, especially calculus and trigonometry.
Video consigliato:
Percorso guidato
5:04
Converting between Degrees & Radians
Understanding π as a Constant
π (pi) is an irrational constant approximately equal to 3.14159, representing the ratio of a circle's circumference to its diameter. Expressing answers as multiples of π keeps the result exact and avoids decimal approximations, which is preferred in trigonometry.
Video consigliato:
Percorso guidato
6:02Stretches and Shrinks of Functions
Simplifying Fractions in Radian Measures
After converting degrees to radians, the resulting fraction involving π should be simplified if possible. Simplifying fractions makes the radian measure clearer and easier to use in further calculations or interpretations.
Video consigliato:
Percorso guidato
5:04Converting between Degrees & Radians
Pratica correlata
Domanda del libro di testo
Find a calculator approximation to four decimal places for each circular function value.
sec 7.3159
730
views
Domanda del libro di testo
Find the exact value of s in the given interval that has the given circular function value.
[ π , 3π/2] ; sec s = ―2√3/3
735
views
Domanda del libro di testo
Find the linear speed v for each of the following.
the tip of the minute hand of a clock, if the hand is 7 cm long
964
views
Domanda del libro di testo
Find each exact function value.
tan π/3
1090
views
Domanda del libro di testo
Find the exact value of s in the given interval that has the given circular function value.
[ 0, π/2] ; cos s = √2/2
744
views