Trigonometry Examples

Find the Asymptotes y=cot(x+pi/2)
Step 1
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 .
Step 2
Subtract from both sides of the equation.
Step 3
Set the inside of the cotangent function equal to .
Step 4
Move all terms not containing to the right side of the equation.
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
To write as a fraction with a common denominator, multiply by .
Step 4.3
Combine and .
Step 4.4
Combine the numerators over the common denominator.
Step 4.5
Simplify the numerator.
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Step 4.5.1
Move to the left of .
Step 4.5.2
Subtract from .
Step 5
The basic period for will occur at , where and are vertical asymptotes.
Step 6
Find the period to find where the vertical asymptotes exist.
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Step 6.1
The absolute value is the distance between a number and zero. The distance between and is .
Step 6.2
Divide by .
Step 7
The vertical asymptotes for occur at , , and every , where is an integer.
Step 8
Cotangent only has vertical asymptotes.
No Horizontal Asymptotes
No Oblique Asymptotes
Vertical Asymptotes: where is an integer
Step 9