Find Amplitude, Period, and Phase Shift y=4sin(3(x-2))+5

$y = 4 \sin (3 (x - 2)) + 5$

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

$a = 4$

$b = 3$

$c = 6$

$d = 5$

Find the amplitude $| a |$ .

Amplitude: $4$

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

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Find the period of $4 \sin (3 x - 6)$ .

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

$\frac{2 π}{| b |}$

Replace $b$ with $3$ in the formula for period.

$\frac{2 π}{| 3 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$\frac{2 π}{3}$

Find the period of $5$ .

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

$\frac{2 π}{| b |}$

Replace $b$ with $3$ in the formula for period.

$\frac{2 π}{| 3 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$\frac{2 π}{3}$

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

$\frac{2 π}{3}$

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: $\frac{6}{3}$

Divide $6$ by $3$ .

Phase Shift: $2$

List the properties of the trigonometric function.

Amplitude: $4$

Period: $\frac{2 π}{3}$

Phase Shift: $2$ ( $2$ to the right)

Vertical Shift: $5$

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Name

Name	one billion six hundred four million one hundred ninety-seven thousand two hundred fifty-seven

Interesting facts

1604197257 has 4 divisors, whose sum is 1645330560
The reverse of 1604197257 is 7527914061
Previous prime number is 39

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 42
Digital Root 6

Name

Name	four hundred thirty-eight million seven hundred sixty-five thousand fifty-three

Interesting facts

438765053 has 8 divisors, whose sum is 465418872
The reverse of 438765053 is 350567834
Previous prime number is 557

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 41
Digital Root 5

Name

Name	one billion nine hundred three million thirty-six thousand seven hundred thirty-two

Interesting facts

1903036732 has 32 divisors, whose sum is 4517679600
The reverse of 1903036732 is 2376303091
Previous prime number is 433

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 34
Digital Root 7

Graph v=11i+11j

Evaluate arcsin(cos(pi/3))

Verify the Identity csc(x)^4-csc(x)^2=cot(x)^4+cot(x)^2

Determine if True 1-cos(80)cos(20)-sin(80)sin(20)=2sin(30)^2

Solve Graphically 2sec(x)+5=9