Find Amplitude, Period, and Phase Shift y=cos(theta-pi)+2

$y = \cos (θ - π) + 2$

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

$a = 1$

$b = 1$

$c = π$

$d = 2$

Find the amplitude $| a |$ .

Amplitude: $1$

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

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Find the period of $\cos (θ - π)$ .

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

$\frac{2 π}{| b |}$

Replace $b$ with $1$ in the formula for period.

$\frac{2 π}{| 1 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$\frac{2 π}{1}$

Divide $2 π$ by $1$ .

$2 π$

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 $1$ in the formula for period.

$\frac{2 π}{| 1 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$\frac{2 π}{1}$

Divide $2 π$ by $1$ .

$2 π$

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

$2 π$

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: $\frac{π}{1}$

Divide $π$ by $1$ .

Phase Shift: $π$

List the properties of the trigonometric function.

Amplitude: $1$

Period: $2 π$

Phase Shift: $π$ ( $π$ to the right)

Vertical Shift: $2$

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Name

Name	one billion three hundred seventy-two million two hundred ten thousand nine hundred twenty-three

Interesting facts

1372210923 has 4 divisors, whose sum is 1829614568
The reverse of 1372210923 is 3290122731
Previous prime number is 3

Basic properties

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

Name

Name	nine hundred seventy million eight hundred eighty-three thousand six hundred ninety-nine

Interesting facts

970883699 has 8 divisors, whose sum is 1006021632
The reverse of 970883699 is 996388079
Previous prime number is 263

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 59
Digital Root 5

Name

Name	one billion two hundred forty-seven million eight hundred ninety-three thousand two hundred nine

Interesting facts

1247893209 has 8 divisors, whose sum is 1437901920
The reverse of 1247893209 is 9023987421
Previous prime number is 9

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 45
Digital Root 9

Find the Exact Value arcsin(-0.79)

Solve the Triangle A=115 , C=35 , c=200

Find the Inverse csc(1.3332)

Expand Using Sum/Difference Formulas cos(45)

Factor over the Complex Numbers (tan(70)h)/5