Textbook Question
Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 30°
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1. Measuring Angles
Radians
Problem 18
Textbook Question
Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ―315°
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: \(-315^\circ \times \frac{\pi}{180}\).
Simplify the fraction \(\frac{315}{180}\) by finding the greatest common divisor (GCD) of 315 and 180, which is 45.
Divide numerator and denominator by 45 to simplify the fraction: \(\frac{315}{180} = \frac{7}{4}\).
Write the final expression for the radian measure as \(-\frac{7\pi}{4}\).
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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 Negative Angles
Negative angles represent rotation in the clockwise direction. When converting negative degrees to radians, the sign is preserved, indicating the direction of rotation. This helps in correctly interpreting the angle's position on the unit circle.
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Expressing Answers as Multiples of π
Leaving answers as multiples of π means expressing the radian measure in terms of π rather than decimal approximations. This exact form is preferred in trigonometry for clarity and precision, such as writing -315° as -7π/4 radians.
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