Textbook Question
CONCEPT PREVIEW Find the radius of each circle.
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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 3.5
Convert each degree measure to radians. Leave answers as multiples of π .
45°
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: \(45^\circ \times \frac{\pi}{180}\).
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.
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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.
Recommended video:
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.
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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.
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5:04Converting between Degrees & Radians
Related Practice
Textbook Question
Find a calculator approximation to four decimal places for each circular function value.
sec 7.3159
Textbook Question
Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
cos s = 0.9250
Textbook Question
Find the linear speed v for each of the following.
a point on the edge of a flywheel of radius 2 m, rotating 42 times per min
Textbook Question
Find the linear speed v for each of the following.
the tip of a propeller 3 m long, rotating 500 times per min (Hint: r = 1.5 m)
Textbook Question
Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.
sin s = 0.4924