Find Amplitude, Period, and Phase Shift f(x)=-5cos(x+2)-5

$f (x) = - 5 \cos (x + 2) - 5$

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

$a = - 5$

$b = 1$

$c = - 2$

$d = - 5$

Find the amplitude $| a |$ .

Amplitude: $5$

Find the period using the formula $\frac{2 π}{| b |}$ .

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Find the period of $- 5 \cos (x + 2)$ .

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The period of the function can be calculated using $\frac{2 π}{| b |}$ .

$\frac{2 π}{| b |}$

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

$\frac{2 π}{| 1 |}$

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

$\frac{2 π}{1}$

Divide $2 π$ by $1$ .

$2 π$

Find the period of $- 5$ .

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The period of the function can be calculated using $\frac{2 π}{| b |}$ .

$\frac{2 π}{| b |}$

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

$\frac{2 π}{| 1 |}$

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

$\frac{2 π}{1}$

Divide $2 π$ by $1$ .

$2 π$

The period of addition/subtraction of trig functions is the maximum of the individual periods.

$2 π$

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: $\frac{- 2}{1}$

Divide $- 2$ by $1$ .

Phase Shift: $- 2$

List the properties of the trigonometric function.

Amplitude: $5$

Period: $2 π$

Phase Shift: $- 2$ ( $2$ to the left)

Vertical Shift: $- 5$

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Name

Name	one billion two hundred seven million five hundred fifty-five thousand five hundred sixty

Interesting facts

1207555560 has 128 divisors, whose sum is 5509684800
The reverse of 1207555560 is 0655557021
Previous prime number is 89

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 36
Digital Root 9

Name

Name	three hundred forty-nine million four hundred ninety-nine thousand eight hundred forty-six

Interesting facts

349499846 has 4 divisors, whose sum is 524249772
The reverse of 349499846 is 648994943
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 56
Digital Root 2

Name

Name	one billion three hundred sixty-one million three hundred seven thousand five hundred thirty-seven

Interesting facts

1361307537 has 32 divisors, whose sum is 2466984960
The reverse of 1361307537 is 7357031631
Previous prime number is 61

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 36
Digital Root 9

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