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: minutes

Problem 7

Textbook Question

In Exercises 5–7, convert each angle in radians to degrees.- 5𝜋6

Verified step by step guidance

Start with the conversion formula: Degrees = Radians × \( \frac{180}{\pi} \).

Substitute the given radian value into the formula: \( 5\pi/6 \times \frac{180}{\pi} \).

Simplify the expression by canceling out \( \pi \) from the numerator and denominator.

Multiply the remaining numbers: \( 5/6 \times 180 \).

Calculate the product 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 or 2π radians. To convert between these units, the relationship is established: 180 degrees equals π radians. Understanding this relationship is essential for converting angles accurately.

Conversion Formula

The conversion from radians to degrees can be done using the formula: degrees = radians × (180/π). This formula allows for straightforward calculations when converting any angle expressed in radians to its equivalent in degrees, ensuring clarity in angular measurements.

Multiplication of Fractions

When converting angles, it often involves multiplying fractions. For example, when converting 5π/6 radians to degrees, you multiply 5π/6 by 180/π. Understanding how to simplify and multiply fractions is crucial for obtaining the correct degree measure from the radian value.