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
Problem 5.28b
Textbook Question
Textbook QuestionUse the given information to find each of the following.
cos θ, given cos 2θ = 1/2 and θ terminates in quadrant II
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Cosine Function
The cosine function, denoted as cos(θ), is a fundamental trigonometric function that relates the angle θ to the ratio of the adjacent side to the hypotenuse in a right triangle. It is periodic and varies between -1 and 1. Understanding the properties of the cosine function is essential for solving problems involving angles and their relationships.
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Double Angle Formula
The double angle formula for cosine states that cos(2θ) = 2cos²(θ) - 1. This formula allows us to express the cosine of a double angle in terms of the cosine of the original angle. It is particularly useful in problems where the value of cos(2θ) is known, enabling the calculation of cos(θ).
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Quadrants and Angle Signs
The unit circle is divided into four quadrants, each affecting the signs of the trigonometric functions. In quadrant II, the cosine function is negative, which is crucial when determining the value of cos(θ) from cos(2θ). Recognizing the quadrant in which the angle terminates helps in accurately identifying the sign of the trigonometric values.
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