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

Angles in Standard Position

Trigonometry

1. Measuring Angles

Angles in Standard Position

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2:13 minutes

Problem 4

Textbook Question

Find a positive angle less than 2𝜋 that is coterminal with16𝜋3

Verified step by step guidance

Understand that coterminal angles are angles that share the same terminal side when drawn in standard position. To find a coterminal angle, you can add or subtract multiples of 2π.

Given the angle \( \frac{16\pi}{3} \), we need to find a positive angle less than \( 2\pi \).

Subtract \( 2\pi \) from \( \frac{16\pi}{3} \) to find a coterminal angle: \( \frac{16\pi}{3} - 2\pi \).

Express \( 2\pi \) with a common denominator: \( 2\pi = \frac{6\pi}{3} \).

Subtract \( \frac{6\pi}{3} \) from \( \frac{16\pi}{3} \) to find the coterminal angle: \( \frac{16\pi}{3} - \frac{6\pi}{3} = \frac{10\pi}{3} \).

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Key Concepts

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

Coterminal Angles

Coterminal angles are angles that share the same terminal side when drawn in standard position. To find a coterminal angle, you can add or subtract multiples of 2π (360 degrees) from the given angle. For example, if you have an angle of 16π/3, you can subtract 2π until the angle falls within the desired range.

Radian Measure

Radian measure is a way of measuring angles based on the radius of a circle. One complete revolution around a circle corresponds to 2π radians. Understanding how to convert between degrees and radians is essential for solving problems involving angles, especially when determining coterminal angles.

Finding Positive Angles

When tasked with finding a positive angle less than 2π, it is important to ensure that the resulting angle is within the range of 0 to 2π. This often involves subtracting 2π from the original angle until the result is positive and falls within the specified range, ensuring that the angle is both coterminal and meets the criteria.