Textbook Question
CONCEPT PREVIEW Find the area of each sector.
Ch. 3 - Radian Measure and The Unit Circle
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- 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
Chapter 4, Problem 9
Convert each degree measure to radians. Leave answers as multiples of π.
800°
Verified step by step guidance1
Recall the conversion formula from degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
Substitute the given degree measure into the formula: \(800^\circ \times \frac{\pi}{180}\).
Simplify the fraction \(\frac{800}{180}\) 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 \(\pi\).
If desired, convert the improper fraction to a mixed number to express the radian measure in a clearer form.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
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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 angles in terms of π allows for exact values rather than decimal approximations, which is useful in trigonometric calculations.
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6:02Stretches and Shrinks of Functions
Simplifying Radicals and Fractions
After converting degrees to radians, the resulting fraction should be simplified by dividing numerator and denominator by their greatest common divisor. This simplification makes the radian measure clearer and easier to interpret, especially when expressed as a multiple of π.
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4:02Solving Linear Equations with Fractions
Related Practice
Textbook Question
CONCEPT PREVIEW Find the area of each sector.
Textbook Question
Use the formula ω = θ/t to find the value of the missing variable.
ω = 2π/3 radians per sec, t = 3 sec
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Textbook Question
Each figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the six circular function values of θ.
Textbook Question
Convert each radian measure to degrees.
5π/4
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Textbook Question
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/2
1
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