Math Problem Statement
Solution
The graph in the image shows a cosecant (csc) function. The cosecant function, , is the reciprocal of the sine function, i.e.,
Analyzing the graph:
- The graph consists of two branches between asymptotes.
- The period (distance between consecutive asymptotes) is , as seen between and .
- The vertical asymptotes appear at , which is typical for a cosecant graph since is undefined wherever .
- The amplitude appears to be 3 (the peak and trough values seem to be and ).
Equation of the graph:
The standard form of a cosecant function is: where:
- controls the amplitude,
- controls the period.
Since the period is , and the amplitude is 3, the equation for the given graph is:
This is the equation for the graph.
Would you like more details, or do you have any further questions?
Relative Questions:
- What is the relationship between sine and cosecant graphs?
- How do vertical asymptotes in cosecant graphs correspond to sine function zeros?
- How does changing the amplitude in affect the graph?
- What happens if the period of a cosecant function is altered?
- Can we shift a cosecant graph horizontally or vertically? How?
Tip: Always remember that cosecant functions have vertical asymptotes where the sine function equals zero, and these asymptotes repeat at every multiple of .
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Cosecant Function
Graph Analysis
Formulas
csc(x) = 1/sin(x)
f(x) = A csc(Bx)
Theorems
Properties of the cosecant function
Suitable Grade Level
High School (Grades 10-12)
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