Find Amplitude, Period, and Phase Shift y=4sin((8x)/5-(5pi)/2)

$y = 4 \sin (\frac{8 x}{5} - \frac{5 π}{2})$

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

$a = 4$

$b = \frac{8}{5}$

$c = \frac{5 π}{2}$

$d = 0$

Find the amplitude $| a |$ .

Amplitude: $4$

Find the period of $4 \sin (\frac{8 x}{5} - \frac{5 π}{2})$ .

Tap for more steps...

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

$\frac{2 π}{| b |}$

Replace $b$ with $\frac{8}{5}$ in the formula for period.

$\frac{2 π}{| \frac{8}{5} |}$

$\frac{8}{5}$ is approximately $1.6$ which is positive so remove the absolute value

$\frac{2 π}{\frac{8}{5}}$

Multiply the numerator by the reciprocal of the denominator.

$2 π \frac{5}{8}$

Cancel the common factor of $2$ .

Tap for more steps...

Factor $2$ out of $2 π$ .

$2 (π) \frac{5}{8}$

Factor $2$ out of $8$ .

$2 (π) \frac{5}{2 (4)}$

Cancel the common factor.

$2 π \frac{5}{2 \cdot 4}$

Rewrite the expression.

$π \frac{5}{4}$

Combine $π$ and $\frac{5}{4}$ .

$\frac{π \cdot 5}{4}$

Move $5$ to the left of $π$ .

$\frac{5 π}{4}$

Find the phase shift using the formula $\frac{c}{b}$ .

Tap for more steps...

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: $\frac{\frac{5 π}{2}}{\frac{8}{5}}$

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: $\frac{5 π}{2} \cdot \frac{5}{8}$

Multiply $\frac{5 π}{2} \cdot \frac{5}{8}$ .

Tap for more steps...

Multiply $\frac{5 π}{2}$ and $\frac{5}{8}$ .

Phase Shift: $\frac{5 π \cdot 5}{2 \cdot 8}$

Multiply $5$ by $5$ .

Phase Shift: $\frac{25 π}{2 \cdot 8}$

Multiply $2$ by $8$ .

Phase Shift: $\frac{25 π}{16}$

List the properties of the trigonometric function.

Amplitude: $4$

Period: $\frac{5 π}{4}$

Phase Shift: $\frac{25 π}{16}$ ( $\frac{25 π}{16}$ to the right)

Vertical Shift: None

Do you know how to Find Amplitude, Period, and Phase Shift y=4sin((8x)/5-(5pi)/2)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name

Name	eight hundred eight million nine hundred twelve thousand six hundred seventy-one

Interesting facts

808912671 has 8 divisors, whose sum is 1232628864
The reverse of 808912671 is 176219808
Previous prime number is 7

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 42
Digital Root 6

Name

Name	one billion one hundred eighteen million nine hundred seventy thousand five hundred ninety-three

Interesting facts

1118970593 has 4 divisors, whose sum is 1205045268
The reverse of 1118970593 is 3950798111
Previous prime number is 13

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 44
Digital Root 8

Name

Name	seven hundred twenty-one million eight hundred ninety-two thousand two hundred forty-eight

Interesting facts

721892248 has 256 divisors, whose sum is 3153572352
The reverse of 721892248 is 842298127
Previous prime number is 101

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 43
Digital Root 7

Evaluate 270*pi/180

Evaluate square root of (1-(-3/5))/(1-3/5)

Find the Reference Angle (11pi)/7

Evaluate 7 square root of 2/2

Simplify sin((5pi)/12)cos(pi/3)+cos((5pi)/12)sin(pi/3)