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
2. Trigonometric Functions on Right Triangles
Trigonometric Functions on Right Triangles
3:35 minutes
Problem 20b
Textbook Question
Textbook QuestionUse the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. See Example 1. sin θ , given that csc θ = √24/3
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Reciprocal Identities
Reciprocal identities in trigonometry relate the sine, cosine, tangent, and their respective cosecant, secant, and cotangent functions. Specifically, the sine function is the reciprocal of the cosecant function, expressed as sin(θ) = 1/csc(θ). Understanding these identities is crucial for converting between different trigonometric functions and solving problems involving them.
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Rationalizing Denominators
Rationalizing the denominator is a technique used to eliminate any radical expressions from the denominator of a fraction. This is often done by multiplying the numerator and denominator by a suitable value that will simplify the expression. In trigonometry, this is important for presenting answers in a standard form, making them easier to interpret and use in further calculations.
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Trigonometric Function Values
Trigonometric function values are the numerical outputs of the sine, cosine, tangent, and their reciprocal functions for a given angle. These values can be derived from known identities or calculated using a calculator. In this context, finding sin(θ) from csc(θ) involves applying the reciprocal identity, which is fundamental for solving trigonometric equations and understanding the relationships between different functions.
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