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
5:52 minutes
Problem 1b
Textbook Question
Textbook QuestionIn Exercises 1–8, a point on the terminal side of angle θ is given. Find the exact value of each of the six trigonometric functions of θ. (-4, 3)
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Trigonometric Functions
The six trigonometric functions—sine, cosine, tangent, cosecant, secant, and cotangent—are fundamental in trigonometry. They relate the angles of a triangle to the ratios of its sides. For a point (x, y) on the terminal side of an angle θ in standard position, these functions can be defined using the coordinates of the point and the radius (r) calculated as r = √(x² + y²).
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Coordinates and the Unit Circle
In trigonometry, the coordinates of a point on the terminal side of an angle θ can be visualized using the unit circle, where the radius is 1. For any point (x, y), the angle θ can be determined, and the coordinates help in finding the values of the trigonometric functions. The unit circle provides a framework for understanding how these functions behave as angles change.
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Pythagorean Theorem
The Pythagorean theorem is essential for calculating the radius (r) when given a point (x, y). It states that in a right triangle, the square of the hypotenuse (r) is equal to the sum of the squares of the other two sides (x and y). This relationship is crucial for determining the exact values of the trigonometric functions based on the coordinates of the point.
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