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CONCEPT PREVIEW Find the area of each sector.
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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 11
Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 60°
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: \(60^\circ \times \frac{\pi}{180}\).
Simplify the fraction \(\frac{60}{180}\) by dividing numerator and denominator by their greatest common divisor, which is 60.
After simplification, express the result as a multiple of \(\pi\).
Write the final answer in radians as a simplified fraction times \(\pi\).
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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 trigonometric applications.
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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 results exact and simplifies further calculations in trigonometry.
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Percorso guidato
6:02Stretches and Shrinks of Functions
Simplifying Fractions
After converting degrees to radians, the resulting fraction involving π should be simplified to its lowest terms. Simplification makes the expression clearer and easier to interpret, such as converting 60° to π/3 radians.
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Percorso guidato
4:02Solving Linear Equations with Fractions
Pratica correlata
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Convert each degree measure to radians. Leave answers as multiples of π.
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