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
5. Inverse Trigonometric Functions and Basic Trigonometric Equations
Inverse Sine, Cosine, & Tangent
Problem 6.25c
Textbook Question
Textbook QuestionEvaluate each expression without using a calculator.
arccos (cos (3π/4))
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Inverse Trigonometric Functions
Inverse trigonometric functions, such as arccos, are used to find the angle whose cosine is a given value. For example, arccos(x) returns the angle θ in the range [0, π] such that cos(θ) = x. Understanding how these functions operate is crucial for evaluating expressions involving them.
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Cosine Function and Its Values
The cosine function, cos(θ), gives the x-coordinate of a point on the unit circle corresponding to the angle θ. For angles like 3π/4, which is in the second quadrant, the cosine value is negative. Recognizing the values of cosine for common angles helps in simplifying expressions involving trigonometric functions.
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Principal Value of Inverse Functions
The principal value of an inverse function refers to the specific output range that the function adheres to. For arccos, the principal value is restricted to [0, π]. This means that when evaluating arccos(cos(3π/4)), one must consider the angle's position within this range to find the correct output.
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