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 25

Chapter 4, Problem 25

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

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: \(-900^\circ \times \frac{\pi}{180}\).

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 \(\frac{\text{integer}}{\text{integer}} \pi\).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Was this helpful?

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.

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.

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.

Recommended video:

6:36

Simplifying Trig Expressions

Related Practice

Textbook Question

Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2.

Halifax, Nova Scotia , 45° N, and Buenos Aires, Argentina, 34° S

views

Textbook Question

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

Textbook Question

Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2.

Farmersville, California, 36° N, and Penticton, British Columbia, 49° N

views

Textbook Question

Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2.

New York City, New York, 41° N, and Lima, Peru, 12° S

views

Textbook Question

Find each exact function value. See Example 2.

cos 7π/4

Textbook Question

Use the formula v = r ω to find the value of the missing variable.

v = 12 m per sec, ω = 3π/2 radians per sec