Find Amplitude, Period, and Phase Shift y=-1/2cos(x-pi)

$y = - \frac{1}{2} \cos (x - π)$

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

$a = - \frac{1}{2}$

$b = 1$

$c = π$

$d = 0$

Find the amplitude $| a |$ .

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

Find the period of $- \frac{\cos (x - π)}{2}$ .

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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 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: $\frac{π}{1}$

Divide $π$ by $1$ .

Phase Shift: $π$

List the properties of the trigonometric function.

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

Period: $2 π$

Phase Shift: $π$ ( $π$ to the right)

Vertical Shift: None

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Name

Name	one billion seven hundred fifty-two million forty-four thousand eighty-two

Interesting facts

1752044082 has 8 divisors, whose sum is 3504088176
The reverse of 1752044082 is 2804402571
Previous prime number is 3

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 33
Digital Root 6

Name

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

Interesting facts

2127254759 has 8 divisors, whose sum is 2448895008
The reverse of 2127254759 is 9574527212
Previous prime number is 137

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 44
Digital Root 8

Name

Name	one billion nine hundred nine million three hundred thirty thousand five

Interesting facts

1909330005 has 32 divisors, whose sum is 3340073088
The reverse of 1909330005 is 5000339091
Previous prime number is 457

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 30
Digital Root 3

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