Find Amplitude, Period, and Phase Shift y=cot(x+(7pi)/6)

$y = \cot (x + \frac{7 π}{6})$

Use the form $a \cot (b x - c) + d$ to find the variables used to find the amplitude, period, phase shift, and vertical shift.

$a = 1$

$b = 1$

$c = - \frac{7 π}{6}$

$d = 0$

Since the graph of the function $c o t$ does not have a maximum or minimum value, there can be no value for the amplitude.

Amplitude: None

Find the period using the formula $\frac{π}{| b |}$ .

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The period of the function can be calculated using $\frac{π}{| b |}$ .

Period: $\frac{π}{| b |}$

Replace $b$ with $1$ in the formula for period.

Period: $\frac{π}{| 1 |}$

Solve the equation.

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The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

Period: $\frac{π}{1}$

Divide $π$ by $1$ .

Period: $π$

Find the phase shift using the formula $\frac{c}{b}$ .

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The phase shift of the function can be calculated from $\frac{c}{b}$ .

Phase Shift: $\frac{c}{b}$

Replace the values of $c$ and $b$ in the equation for phase shift.

Phase Shift: $\frac{- \frac{7 π}{6}}{1}$

Divide $- \frac{7 π}{6}$ by $1$ .

Phase Shift: $- \frac{7 π}{6}$

Find the vertical shift $d$ .

Vertical Shift: $0$

List the properties of the trigonometric function.

Amplitude: None

Period: $π$

Phase Shift: $- \frac{7 π}{6}$ ( $\frac{7 π}{6}$ to the left)

Vertical Shift: $0$

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Name

Name	one billion seven hundred fifty-five million nine hundred ninety-four thousand two hundred seven

Interesting facts

1755994207 has 8 divisors, whose sum is 1962353232
The reverse of 1755994207 is 7024995571
Previous prime number is 41

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 49
Digital Root 4

Name

Name	one billion seven hundred ninety-seven million seven hundred seven thousand nine hundred seventy

Interesting facts

1797707970 has 16 divisors, whose sum is 2851540920
The reverse of 1797707970 is 0797077971
Previous prime number is 29

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 54
Digital Root 9

Name

Name	one billion eight hundred ninety-seven million five hundred twenty-five thousand six hundred seventy-five

Interesting facts

1897525675 has 16 divisors, whose sum is 2733069600
The reverse of 1897525675 is 5765257981
Previous prime number is 7649

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 55
Digital Root 1

Factor f(x)=3x^3-16x^2-103x+36

Verify the Identity (tan(x)^2+1)(cos(x)^2-1)=-tan(x)^2

Graph y>-9

Graph (x-2)^2+(y+1)^2=0

Graph y=2sin(3(x+pi/12))+4