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
Trigonometric Functions on the Unit Circle
3:45 minutes
Problem 5
Textbook Question
Textbook QuestionCONCEPT PREVIEW Match each trigonometric function in Column I with its value in Column II. Choices may be used once, more than once, or not at all. I II 1. A. √3 2. B. 1 3. C. ½ 4. D. √3 5. csc 60° 2 6. E. 2√3 3 F. √3 3 G. 2 H. √2 2 I. √2
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Trigonometric Functions
Trigonometric functions relate the angles of a triangle to the lengths of its sides. The primary functions include sine (sin), cosine (cos), and tangent (tan), along with their reciprocals: cosecant (csc), secant (sec), and cotangent (cot). Understanding these functions is essential for solving problems involving angles and side lengths in right triangles.
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Special Angles
Certain angles, such as 30°, 45°, and 60°, have known sine, cosine, and tangent values that are often used in trigonometry. For example, sin 60° equals √3/2, and csc 60° is the reciprocal, which equals 2. Familiarity with these special angles allows for quicker calculations and a deeper understanding of trigonometric relationships.
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Reciprocal Identities
Reciprocal identities in trigonometry define relationships between the primary trigonometric functions and their reciprocals. For instance, cosecant is the reciprocal of sine, meaning csc θ = 1/sin θ. Recognizing these identities is crucial for solving trigonometric equations and simplifying expressions, especially when matching functions to their values.
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