Math Problem Statement
y=2tan3x
Solution
The equation is a trigonometric function. Let's break it down:
General Form
The tangent function, , has the following key properties:
- Amplitude: The tangent function does not have a defined amplitude because it increases and decreases without bound.
- Period: The period is given by . Here, , so the period is:
- Vertical Stretch/Compression: The factor scales the tangent function vertically, making its slope twice as steep.
Key Points
The function includes these features:
- Period:
- Vertical Asymptotes: The vertical asymptotes occur where , or , where is an integer.
- Scaling: The graph of is stretched vertically by a factor of 2.
Graph Overview
The graph will:
- Pass through , since .
- Repeat its pattern every .
- Have vertical asymptotes at .
Would you like me to:
- Graph the function?
- Derive its derivative ?
- Solve for specific values of ?
- Analyze domain and range?
- Discuss its practical applications?
Tip: For any tangent function, understanding the period and asymptotes helps you sketch and interpret the graph more effectively.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Graphing Functions
Tangent Function Properties
Formulas
Period of tangent function: Period = π / k
Vertical asymptotes: x = (π/2 + nπ) / k
Theorems
Properties of tangent function
Suitable Grade Level
Grades 10-12