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Ch. 3 - Radian Measure and The Unit Circle
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. 3 - Radian Measure and The Unit CircleProblema 25
Capitolo 4, Problema 25

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ―900°

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1
Recall the formula to convert degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
Substitute the given degree measure into the formula: \(-900^\circ \times \frac{\pi}{180}\).
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor.
Express the result as a multiple of \(\pi\) without calculating the decimal value.
Write the final answer in the form \(\frac{\text{integer}}{\text{integer}} \pi\).

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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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Converting between Degrees & Radians

Understanding Negative Angles

Negative angles represent rotation in the clockwise direction, opposite to the positive (counterclockwise) direction. When converting, the sign is preserved, indicating the direction of rotation, which is important for interpreting the angle correctly.
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Coterminal Angles

Expressing Answers as Multiples of π

Leaving answers as multiples of π means writing 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 -900° as -5π radians.
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Simplifying Trig Expressions
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