Find Amplitude, Period, and Phase Shift y=4sin((x-pi)/4)-3

$y = 4 \sin (\frac{x - π}{4}) - 3$

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

$a = 4$

$b = \frac{1}{4}$

$c = \frac{π}{4}$

$d = - 3$

Find the amplitude $| a |$ .

Amplitude: $4$

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

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Find the period of $4 \sin (\frac{x - π}{4})$ .

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

$\frac{2 π}{| b |}$

Replace $b$ with $\frac{1}{4}$ in the formula for period.

$\frac{2 π}{| \frac{1}{4} |}$

$\frac{1}{4}$ is approximately $0.25$ which is positive so remove the absolute value

$\frac{2 π}{\frac{1}{4}}$

Multiply the numerator by the reciprocal of the denominator.

$2 π \cdot 4$

Multiply $4$ by $2$ .

$8 π$

Find the period of $- 3$ .

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

$\frac{2 π}{| b |}$

Replace $b$ with $\frac{1}{4}$ in the formula for period.

$\frac{2 π}{| \frac{1}{4} |}$

$\frac{1}{4}$ is approximately $0.25$ which is positive so remove the absolute value

$\frac{2 π}{\frac{1}{4}}$

Multiply the numerator by the reciprocal of the denominator.

$2 π \cdot 4$

Multiply $4$ by $2$ .

$8 π$

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

$8 π$

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: $\frac{\frac{π}{4}}{\frac{1}{4}}$

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: $\frac{π}{4} \cdot 4$

Cancel the common factor of $4$ .

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Cancel the common factor.

Phase Shift: $\frac{π}{4} \cdot 4$

Rewrite the expression.

Phase Shift: $π$

List the properties of the trigonometric function.

Amplitude: $4$

Period: $8 π$

Phase Shift: $π$ ( $π$ to the right)

Vertical Shift: $- 3$

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Name

Name	one billion eight hundred sixteen million one hundred three thousand four hundred four

Interesting facts

1816103404 has 16 divisors, whose sum is 4326599448
The reverse of 1816103404 is 4043016181
Previous prime number is 17

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 28
Digital Root 1

Name

Name	one billion four hundred fifty-five million four hundred thirteen thousand three hundred seventy-two

Interesting facts

1455413372 has 32 divisors, whose sum is 3871545120
The reverse of 1455413372 is 2733145541
Previous prime number is 29

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 35
Digital Root 8

Name

Name	two hundred seventy-four million seven hundred forty thousand eight hundred ninety-one

Interesting facts

274740891 has 4 divisors, whose sum is 366321192
The reverse of 274740891 is 198047472
Previous prime number is 3

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 42
Digital Root 6

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