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
6. Trigonometric Identities and More Equations
Introduction to Trigonometric Identities
4:22 minutes
Problem 51
Textbook Question
Textbook QuestionIn Exercises 47–54, use the figures to find the exact value of each trigonometric function. α cos ------- 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, such as sine, cosine, and tangent, relate the angles of a triangle to the lengths of its sides. These functions are fundamental in trigonometry and are defined for right triangles, where the cosine of an angle is the ratio of the adjacent side to the hypotenuse. Understanding these functions is essential for solving problems involving angles and distances.
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Cosine Function
The cosine function is one of the primary trigonometric functions, denoted as cos(θ), where θ is an angle. It is defined as the ratio of the length of the adjacent side to the hypotenuse in a right triangle. In the context of the question, finding the exact value of cos(α/2) requires knowledge of angle relationships and possibly the use of trigonometric identities.
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Trigonometric Identities
Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables involved. Key identities include the Pythagorean identity, angle sum and difference identities, and double angle formulas. These identities are crucial for simplifying expressions and solving trigonometric equations, particularly when calculating values like cos(α/2).
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