Ch. 3 - Radian Measure and The Unit Circle

Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook

Lial 12th Edition

Ch. 3 - Radian Measure and The Unit Circle

Problem 26

Chapter 4, Problem 26

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ―1800°

Verified step by step guidance

Recall the formula to convert degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).

Substitute the given degree measure into the formula: \(1800^\circ \times \frac{\pi}{180}\).

Simplify the fraction by dividing 1800 by 180: \(\frac{1800}{180} = 10\).

Express the result as a multiple of \(\pi\): \(10\pi\) radians.

Therefore, the degree measure \(1800^\circ\) is equivalent to \(10\pi\) radians.

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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.

Understanding Multiples of π

Expressing angles as multiples of π simplifies the representation of radian measures. Since π radians equal 180°, converting degrees to radians often results in fractions involving π, which should be left in this form for exactness and clarity.

Simplifying Fractions

After converting degrees to radians, the resulting fraction should be simplified to its lowest terms. This makes the radian measure easier to interpret and use in further calculations, ensuring the answer is presented in the simplest exact form.

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