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The formula ω = θ/t can be rewritten as θ = ωt. Substituting ωt for θ converts s = rθ to s = rωt. Use the formula s = rωt to find the value of the missing variable.
s = 3π/4 km, r = 2 km, t = 4 sec
618
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Ch. 3 - Radian Measure and The Unit Circle
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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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 33
Convert each radian measure to degrees. See Examples 2(a) and 2(b). 11π/6
Guida verificata passo dopo passo1
Recall the conversion formula between radians and degrees: \(\text{Degrees} = \text{Radians} \times \frac{180}{\pi}\).
Identify the given radian measure: \(\frac{11\pi}{6}\).
Substitute the radian value into the conversion formula: \(\frac{11\pi}{6} \times \frac{180}{\pi}\).
Simplify the expression by canceling \(\pi\) in numerator and denominator: \(\frac{11}{6} \times 180\).
Multiply the fraction by 180 to find the degree measure: \(11 \times \frac{180}{6}\).
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Radian Measure
A radian is a unit of angular measure based on the radius of a circle. One radian is the angle created when the arc length equals the radius. It is a standard unit in trigonometry, where 2π radians equal 360 degrees.
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5:04
Converting between Degrees & Radians
Degree Measure
Degrees are a common unit for measuring angles, where a full circle is divided into 360 equal parts. Each degree can be further divided into minutes and seconds, but for most trigonometry problems, degrees are used as a straightforward measure of angle size.
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5:04Converting between Degrees & Radians
Conversion Between Radians and Degrees
To convert radians to degrees, multiply the radian measure by 180/π. This ratio comes from the equivalence of 2π radians to 360 degrees. For example, 11π/6 radians equals (11π/6) × (180/π) = 330 degrees.
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5:04Converting between Degrees & Radians
Pratica correlata
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Convert each radian measure to degrees. See Examples 2(a) and 2(b). 7π/4
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Domanda del libro di testo
Find a calculator approximation to four decimal places for each circular function value. See Example 3. cos (-1.1519)
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Domanda del libro di testo
Find a calculator approximation to four decimal places for each circular function value. See Example 3. sin 0.6109
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Domanda del libro di testo
Convert each radian measure to degrees. See Examples 2(a) and 2(b). ―π/6
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Domanda del libro di testo
Find each exact function value. See Example 2.
tan 5π/6
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