Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

1. Measuring Angles

Radians

Trigonometry

1. Measuring Angles

Radians

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2:11 minutes

Problem 16

Textbook Question

In Exercises 13–20, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋.150°

Verified step by step guidance

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

Substitute the given angle in degrees (150°) into the formula: \( 150 \times \frac{\pi}{180} \).

Simplify the fraction \( \frac{150}{180} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 30.

This simplification gives \( \frac{5}{6} \).

Therefore, the angle in radians is \( \frac{5\pi}{6} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Degrees and Radians

Degrees and radians are two units for measuring angles. A full circle is 360 degrees, which is equivalent to 2π radians. Understanding the relationship between these two units is essential for converting angles from one to the other.

Conversion Formula

To convert degrees to radians, the formula used is: radians = degrees × (π/180). This formula allows for the direct conversion of any angle measured in degrees into its corresponding value in radians.

Multiples of π

When expressing angles in radians, it is common to represent them as multiples of π. This means that the radian measure is expressed in terms of π, such as nπ, where n is a rational number. This format is particularly useful in trigonometry for simplifying expressions and solving equations.