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 3.47
Textbook Question
Textbook QuestionFind a calculator approximation to four decimal places for each circular function value. cos (-0.2443)
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Circular Functions
Circular functions, also known as trigonometric functions, relate the angles of a circle to the ratios of its sides. The primary circular functions include sine, cosine, and tangent, which are defined based on the unit circle. For any angle θ, the cosine function, cos(θ), represents the x-coordinate of the point on the unit circle corresponding to that angle.
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Graphs of Common Functions
Negative Angles
In trigonometry, negative angles indicate a clockwise rotation from the positive x-axis. The cosine function is an even function, meaning that cos(-θ) = cos(θ). This property allows us to simplify calculations involving negative angles by using their positive counterparts, making it easier to find values for functions like cos(-0.2443).
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Calculator Approximations
Calculator approximations for trigonometric functions provide numerical values for angles that may not correspond to simple fractions or known values. Most scientific calculators can compute these values to a specified number of decimal places. For instance, finding cos(-0.2443) requires inputting the angle into the calculator and rounding the result to four decimal places for precision.
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