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
3:56 minutes
Problem 49
Textbook Question
Textbook QuestionIn Exercises 47–54, use the figures to find the exact value of each trigonometric function. θ tan ------- 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), which are defined as ratios of the sides of a right triangle. Understanding these functions is essential for solving problems involving angles and distances in trigonometry.
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Tangent Function
The tangent function is defined as the ratio of the opposite side to the adjacent side in a right triangle. It can also be expressed in terms of sine and cosine as tan(θ) = sin(θ) / cos(θ). Knowing how to calculate and interpret the tangent function is crucial for finding exact values in trigonometric problems.
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Exact Values of Trigonometric Functions
Exact values of trigonometric functions refer to specific values that can be determined without approximation, often using special angles like 0°, 30°, 45°, 60°, and 90°. These values are typically derived from the unit circle or special right triangles, and they are fundamental for solving trigonometric equations and problems accurately.
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