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 7
Convert each degree measure to radians. Leave answers as multiples of π.
175°
Verified step by step guidance1
Recall the formula to convert degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
Substitute the given degree measure into the formula: \(175^\circ \times \frac{\pi}{180}\).
Simplify the fraction \(\frac{175}{180}\) by finding the greatest common divisor (GCD) of 175 and 180.
Express the simplified fraction multiplied by \(\pi\) to write the answer as a multiple of \(\pi\).
Write the final answer in the form \(\frac{a}{b} \pi\), where \(a\) and \(b\) are the simplified numerator and denominator.
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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 as multiples of π provides an exact and simplified form, which is preferred over decimal approximations in trigonometry.
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Simplifying Fractions in Angle Conversion
After converting degrees to radians, the resulting fraction should be simplified to its lowest terms. Simplification makes the expression clearer and easier to work with in further calculations, such as solving trigonometric equations or evaluating functions.
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4:02Solving Linear Equations with Fractions
Related Practice
Textbook Question
CONCEPT PREVIEW Find the area of each sector.
Textbook Question
CONCEPT PREVIEW Find the measure of each central angle (in radians).
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
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
CONCEPT PREVIEW Find the measure of each central angle (in radians).
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