Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles39m
- 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
3. Unit Circle
Defining the Unit Circle
Problem 3.27bLial - 12th Edition
Textbook Question
Textbook QuestionFind each exact function value. See Example 2.
sin (4π/3)
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Unit Circle
The unit circle is a circle with a radius of one centered at the origin of a coordinate plane. It is fundamental in trigonometry as it allows us to define the sine, cosine, and tangent functions for all angles. The coordinates of points on the unit circle correspond to the cosine and sine values of the angle formed with the positive x-axis.
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Introduction to the Unit Circle
Reference Angles
A reference angle is the acute angle formed by the terminal side of an angle and the x-axis. It is used to simplify the calculation of trigonometric functions for angles greater than 90 degrees or less than 0 degrees. For example, the reference angle for 4π/3 radians is π/3, which helps in determining the sine value.
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Reference Angles on the Unit Circle
Sine Function
The sine function, denoted as sin(θ), represents the ratio of the length of the opposite side to the hypotenuse in a right triangle. On the unit circle, it corresponds to the y-coordinate of a point at a given angle θ. Understanding the sine function is crucial for finding exact values, especially for angles like 4π/3, which lies in the third quadrant where sine values are negative.
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Graph of Sine and Cosine Function
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Related Practice
Textbook Question
In Exercises 1–4, a point P(x, y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t.
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Defining the Unit Circle practice set
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