Find Amplitude, Period, and Phase Shift y=3sin(theta/4)-2

$y = 3 \sin (\frac{θ}{4}) - 2$

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

$a = 3$

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

$c = 0$

$d = - 2$

Find the amplitude $| a |$ .

Amplitude: $3$

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

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Find the period of $3 \sin (\frac{θ}{4})$ .

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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 $- 2$ .

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

$\frac{2 π}{| b |}$

Replace $b$ with $\frac{1}{4}$ 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: $\frac{0}{\frac{1}{4}}$

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: $0 \cdot 4$

Multiply $0$ by $4$ .

Phase Shift: $0$

List the properties of the trigonometric function.

Amplitude: $3$

Period: $8 π$

Phase Shift: None

Vertical Shift: $- 2$

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Name

Name	one billion two hundred eighty-two million nine hundred fifty-five thousand eight hundred twenty-nine

Interesting facts

1282955829 has 8 divisors, whose sum is 1312767360
The reverse of 1282955829 is 9285592821
Previous prime number is 179

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 51
Digital Root 6

Name

Name	one billion four hundred ninety-nine million six hundred thirty-six thousand four hundred fifty-four

Interesting facts

1499636454 has 8 divisors, whose sum is 2999272920
The reverse of 1499636454 is 4546369941
Previous prime number is 3

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 51
Digital Root 6

Name

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

Interesting facts

1242107984 has 64 divisors, whose sum is 6771878316
The reverse of 1242107984 is 4897012421
Previous prime number is 13

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 38
Digital Root 2

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