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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1:52 minutes

Problem 68

Textbook Question

In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle.-𝜋40

Verified step by step guidance

Step 1: 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 full rotations (in radians, this is 2\pi) from the given angle.

Step 2: The given angle is -\pi. We need to find a positive angle less than 2\pi that is coterminal with -\pi.

Step 3: Add 2\pi to the given angle -\pi to find a positive coterminal angle: -\pi + 2\pi.

Step 4: Simplify the expression from Step 3 to find the positive coterminal angle.

Step 5: Verify that the resulting angle is positive and less than 2\pi.

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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 (or 360 degrees) from the given angle. For example, if you have an angle of -π, adding 2π results in a positive coterminal angle.

Radians and Degrees

Angles can be measured in radians or degrees, with 2π radians equivalent to 360 degrees. Understanding the relationship between these two units is crucial for converting angles and finding coterminal angles. In this case, -π radians is equivalent to -180 degrees, which helps in visualizing the angle's position on the unit circle.

Unit Circle

The unit circle is a circle with a radius of one centered at the origin of a coordinate plane. It is a fundamental tool in trigonometry for understanding angles and their corresponding sine, cosine, and tangent values. By visualizing angles on the unit circle, one can easily determine coterminal angles and their properties.