Graph 1/(2cot(2x))

Graph 1/(2cot(2x))
Find the asymptotes.
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 tangent function, , for equal to to find where the vertical asymptote occurs for .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Multiply .
Multiply and .
Multiply by .
Set the inside of the tangent function equal to .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Multiply .
Multiply and .
Multiply 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.
Tangent only has vertical asymptotes.
No Horizontal Asymptotes
No Oblique Asymptotes
Vertical Asymptotes: where is an integer
No Horizontal Asymptotes
No Oblique Asymptotes
Vertical Asymptotes: where is an integer
Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.
Since the graph of the function does not have a maximum or minimum value, there can be no value for the amplitude.
Amplitude: None
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Find the phase shift using the formula .
The phase shift of the function can be calculated from .
Phase Shift:
Replace the values of and in the equation for phase shift.
Phase Shift:
Divide by .
Phase Shift:
Phase Shift:
Find the vertical shift .
Vertical Shift:
List the properties of the trigonometric function.
Amplitude: None
Period:
Phase Shift: ( to the right)
Vertical Shift:
The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.
Vertical Asymptotes: where is an integer
Amplitude: None
Period:
Phase Shift: ( to the right)
Vertical Shift:
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Name

Name six hundred ninety-four million six hundred seventy-seven thousand three hundred fifty-one

Interesting facts

• 694677351 has 4 divisors, whose sum is 926236472
• The reverse of 694677351 is 153776496
• Previous prime number is 3

Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 48
• Digital Root 3

Name

Name one hundred forty-seven million six hundred forty-five thousand four hundred fifty

Interesting facts

• 147645450 has 32 divisors, whose sum is 341228160
• The reverse of 147645450 is 054546741
• Previous prime number is 25

Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 36
• Digital Root 9

Name

Name one billion five hundred seventy-nine million nine hundred six thousand two hundred fifty-eight

Interesting facts

• 1579906258 has 32 divisors, whose sum is 2860830720
• The reverse of 1579906258 is 8526099751
• Previous prime number is 43

Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 52
• Digital Root 7