Find Amplitude, Period, and Phase Shift y=3sin(pix-1/2)

$y = 3 \sin (π x - \frac{1}{2})$

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

$a = 3$

$b = π$

$c = \frac{1}{2}$

$d = 0$

Find the amplitude $| a |$ .

Amplitude: $3$

Find the period of $3 \sin (π x - \frac{1}{2})$ .

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

$\frac{2 π}{| b |}$

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

$\frac{2 π}{| π |}$

$π$ is approximately $3.14159265$ which is positive so remove the absolute value

$\frac{2 π}{π}$

Cancel the common factor of $π$ .

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Cancel the common factor.

$\frac{2 π}{π}$

Divide $2$ by $1$ .

$2$

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: $\frac{\frac{1}{2}}{π}$

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: $\frac{1}{2} \cdot \frac{1}{π}$

Multiply $\frac{1}{2}$ and $\frac{1}{π}$ .

Phase Shift: $\frac{1}{2 π}$

List the properties of the trigonometric function.

Amplitude: $3$

Period: $2$

Phase Shift: $\frac{1}{2 π}$ ( $\frac{1}{2 π}$ to the right)

Vertical Shift: None

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Name

Name	one billion six hundred eighty-four million one hundred forty-three thousand twenty-one

Interesting facts

1684143021 has 8 divisors, whose sum is 2248573824
The reverse of 1684143021 is 1203414861
Previous prime number is 737

Basic properties

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

Name

Name	one billion ninety-seven million two hundred thirty-five thousand one hundred eighty-four

Interesting facts

1097235184 has 128 divisors, whose sum is 5762016000
The reverse of 1097235184 is 4815327901
Previous prime number is 389

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 40
Digital Root 4

Name

Name	three hundred forty-seven million nine hundred fifty-five thousand fifty-eight

Interesting facts

347955058 has 8 divisors, whose sum is 569381040
The reverse of 347955058 is 850559743
Previous prime number is 11

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 46
Digital Root 1

Simplify (sin(y)^2)/(1-cos(y))

Find the Inverse y=1/2*sin(x)

Graph -cot(11x)

Solve Graphically sin(2x)=0.5

Find the Sine (0.24,0.45)