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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1:56 minutes

Problem 5

Textbook Question

In Exercises 5–7, convert each angle in radians to degrees.5𝜋3

Verified step by step guidance

Recall the conversion factor between radians and degrees: $180^\circ = \pi$ radians.

To convert an angle from radians to degrees, multiply the radian measure by $\frac{180^\circ}{\pi}$.

Given the angle $\frac{5\pi}{3}$ radians, apply the conversion: $\frac{5\pi}{3} \times \frac{180^\circ}{\pi}$.

Simplify the expression by canceling out $\pi$ in the numerator and denominator.

Multiply the remaining numbers to find the angle in degrees.

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Key Concepts

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

Radians and Degrees

Radians and degrees are two units for measuring angles. A full circle is 360 degrees, which is equivalent to 2π radians. To convert between these units, one can use the relationship that 180 degrees equals π radians.

Conversion Formula

The conversion from radians to degrees can be performed using the formula: degrees = radians × (180/π). This formula allows for the straightforward transformation of an angle measured in radians into its degree equivalent.

Simplifying Fractions

When converting angles, it is often necessary to simplify fractions. For example, when converting 5π/3 radians, one should first multiply by the conversion factor and then simplify the resulting fraction to express the angle in its simplest degree form.