Textbook Question
Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 90°
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1. Measuring Angles
Radians
Problem 19
Textbook Question
Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 450°
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: \(450^\circ \times \frac{\pi}{180}\).
Simplify the fraction \(\frac{450}{180}\) 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 \(k\pi\), where \(k\) is the simplified fraction obtained in the previous step.
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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 trigonometric applications.
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Understanding Multiples of π
Expressing angles as multiples of π simplifies trigonometric calculations and provides exact values. Instead of decimal approximations, answers like 5π/2 represent precise angle measures in radians.
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Simplifying Fractions
After converting degrees to radians, the resulting fraction should be simplified to its lowest terms. This makes the expression cleaner and easier to interpret, especially when working with multiples of π.
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