Find Amplitude, Period, and Phase Shift y=3sin(2x+3pi)-1

$y = 3 \sin (2 x + 3 π) - 1$

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

$a = 3$

$b = 2$

$c = - 3 π$

$d = - 1$

Find the amplitude $| a |$ .

Amplitude: $3$

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

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Find the period of $3 \sin (2 x + 3 π)$ .

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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 $- 1$ .

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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: $\frac{- 3 π}{2}$

Move the negative in front of the fraction.

Phase Shift: $- \frac{3 π}{2}$

List the properties of the trigonometric function.

Amplitude: $3$

Period: $π$

Phase Shift: $- \frac{3 π}{2}$ ( $\frac{3 π}{2}$ to the left)

Vertical Shift: $- 1$

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Name

Name	two billion one hundred eleven million six hundred sixty-six thousand two hundred nineteen

Interesting facts

2111666219 has 8 divisors, whose sum is 2311383312
The reverse of 2111666219 is 9126661112
Previous prime number is 61

Basic properties

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

Name

Name	eight hundred eighty-six million one hundred thirty-three thousand one hundred forty

Interesting facts

886133140 has 32 divisors, whose sum is 2469740544
The reverse of 886133140 is 041331688
Previous prime number is 31

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 34
Digital Root 7

Name

Name	six hundred forty-two million one hundred two thousand five hundred sixteen

Interesting facts

642102516 has 16 divisors, whose sum is 1459324800
The reverse of 642102516 is 615201246
Previous prime number is 99

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 27
Digital Root 9

Convert from Radians to Degrees -(17pi)/9

Simplify square root of x+(x-3)

Expand the Logarithmic Expression log base b of ninth root of (x^4)/(y^9x^5)

Solve the Triangle a=8 , c=7 , B=31.8

Simplify ((cos(x))/(sin(x)))/(cos(x))