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Trigonometry Examples
Step 1
Step 1.1
Divide each term in by .
Step 1.2
Simplify the left side.
Step 1.2.1
Cancel the common factor of .
Step 1.2.1.1
Cancel the common factor.
Step 1.2.1.2
Divide by .
Step 2
Find where the expression is undefined.
Step 3
Consider the rational function where is the degree of the numerator and is the degree of the denominator.
1. If , then the x-axis, , is the horizontal asymptote.
2. If , then the horizontal asymptote is the line .
3. If , then there is no horizontal asymptote (there is an oblique asymptote).
Step 4
Find and .
Step 5
Since , the x-axis, , is the horizontal asymptote.
Step 6
Use polynomial division to find the oblique asymptotes. Because this expression contains a radical, polynomial division cannot be performed.
Cannot Find Oblique Asymptotes
Step 7
This is the set of all asymptotes.
Vertical Asymptotes:
Horizontal Asymptotes:
Cannot Find Oblique Asymptotes
Step 8