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
5. Inverse Trigonometric Functions and Basic Trigonometric Equations
Linear Trigonometric Equations
6:11 minutes
Problem 83
Textbook Question
Textbook QuestionIn Exercises 63β84, use an identity to solve each equation on the interval [0, 2π ). tan x + sec x = 1
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Trigonometric Identities
Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variable where both sides of the equation are defined. Key identities include the Pythagorean identities, reciprocal identities, and co-function identities. Understanding these identities is crucial for simplifying trigonometric expressions and solving equations, as they allow for the transformation of one function into another.
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Fundamental Trigonometric Identities
Tangent and Secant Functions
The tangent function, defined as the ratio of the sine and cosine functions (tan x = sin x / cos x), represents the slope of the angle in a right triangle. The secant function, which is the reciprocal of the cosine function (sec x = 1 / cos x), is used to relate angles to their corresponding sides in a triangle. Recognizing the relationship between these functions is essential for manipulating and solving equations involving them.
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Graphs of Secant and Cosecant Functions
Solving Trigonometric Equations
Solving trigonometric equations involves finding the angles that satisfy the equation within a specified interval. This process often requires the use of identities to rewrite the equation in a more manageable form. Techniques such as factoring, using inverse functions, and applying known values of trigonometric functions are commonly employed to isolate the variable and determine the solutions.
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How to Solve Linear Trigonometric Equations
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