Find Amplitude, Period, and Phase Shift f(x)=2sin(2x)-pi/2

$f (x) = 2 \sin (2 x) - \frac{π}{2}$

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

$a = 2$

$b = 2$

$c = 0$

$d = - \frac{π}{2}$

Find the amplitude $| a |$ .

Amplitude: $2$

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

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Find the period of $2 \sin (2 x)$ .

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

$\frac{2 π}{| b |}$

Replace $b$ with $2$ in the formula for period.

$\frac{2 π}{| 2 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$\frac{2 π}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 π}{2}$

Divide $π$ by $1$ .

$π$

Find the period of $- \frac{π}{2}$ .

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

$\frac{2 π}{| b |}$

Replace $b$ with $2$ in the formula for period.

$\frac{2 π}{| 2 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$\frac{2 π}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 π}{2}$

Divide $π$ by $1$ .

$π$

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

$π$

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: $\frac{0}{2}$

Divide $0$ by $2$ .

Phase Shift: $0$

List the properties of the trigonometric function.

Amplitude: $2$

Period: $π$

Phase Shift: None

Vertical Shift: $- \frac{π}{2}$

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Name

Name	two billion fifty-three million three hundred ninety-three thousand five hundred seventy-seven

Interesting facts

2053393577 has 4 divisors, whose sum is 2101146960
The reverse of 2053393577 is 7753933502
Previous prime number is 43

Basic properties

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

Name

Name	nine hundred eight million one hundred one thousand five hundred thirty-three

Interesting facts

908101533 has 8 divisors, whose sum is 1211805088
The reverse of 908101533 is 335101809
Previous prime number is 249547

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 30
Digital Root 3

Name

Name	one billion five hundred fifty-eight million nine hundred forty-four thousand nine hundred twenty-six

Interesting facts

1558944926 has 32 divisors, whose sum is 3009484800
The reverse of 1558944926 is 6294498551
Previous prime number is 11

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 53
Digital Root 8

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