Trigonometry Examples

Find the Asymptotes 3cot(2x)-4
For any , vertical asymptotes occur at , where is an integer. Use the basic period for , , to find the vertical asymptotes for . Set the inside of the cotangent function, , for equal to to find where the vertical asymptote occurs for .
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Divide by .
Set the inside of the cotangent function equal to .
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
The basic period for will occur at , where and are vertical asymptotes.
The absolute value is the distance between a number and zero. The distance between and is .
The vertical asymptotes for occur at , , and every , where is an integer.
Cotangent only has vertical asymptotes.
No Horizontal Asymptotes
No Oblique Asymptotes
Vertical Asymptotes: where is an integer
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