Find Amplitude, Period, and Phase Shift y=(2pi)/3sec(3x)

$y = \frac{2 π}{3} \sec (3 x)$

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

$a = \frac{2 π}{3}$

$b = 3$

$c = 0$

$d = 0$

Since the graph of the function $s e c$ does not have a maximum or minimum value, there can be no value for the amplitude.

Amplitude: None

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

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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 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: $\frac{0}{3}$

Divide $0$ by $3$ .

Phase Shift: $0$

List the properties of the trigonometric function.

Amplitude: None

Period: $\frac{2 π}{3}$

Phase Shift: None

Vertical Shift: None

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Name

Name	seven hundred forty-six million eight hundred fifty-four thousand three hundred seventy-four

Interesting facts

746854374 has 64 divisors, whose sum is 2229682176
The reverse of 746854374 is 473458647
Previous prime number is 7

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 48
Digital Root 3

Name

Name	one billion eight million six hundred ten thousand four hundred thirteen

Interesting facts

1008610413 has 8 divisors, whose sum is 1363236288
The reverse of 1008610413 is 3140168001
Previous prime number is 73

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 24
Digital Root 6

Name

Name	one hundred sixty-five million five hundred eighty-two thousand three hundred six

Interesting facts

165582306 has 32 divisors, whose sum is 490614720
The reverse of 165582306 is 603285561
Previous prime number is 3

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 36
Digital Root 9

Determine if Linear y=-2cos(x)

Graph y=-3+4cos(pi(x-2))

Solve for c arccos(90)=16/c

Graph f(x)=2 log base 5 of x+3-1

Simplify cos(arcsin(5/13))