Find Amplitude, Period, and Phase Shift y=-5tan(3x+pi)

$y = - 5 \tan (3 x + π)$

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

$a = - 5$

$b = 3$

$c = - π$

$d = 0$

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

Amplitude: None

Find the period of $- 5 \tan (3 x + π)$ .

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

$\frac{π}{| b |}$

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

$\frac{π}{| 3 |}$

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

$\frac{π}{3}$

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: $\frac{- π}{3}$

Move the negative in front of the fraction.

Phase Shift: $- \frac{π}{3}$

List the properties of the trigonometric function.

Amplitude: None

Period: $\frac{π}{3}$

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

Vertical Shift: None

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Name

Name	one million six hundred sixty-two thousand nine hundred sixty-two

Interesting facts

1662962 has 16 divisors, whose sum is 2592000
The reverse of 1662962 is 2692661
Previous prime number is 71

Basic properties

Is Prime? no
Number parity even
Number length 7
Sum of Digits 32
Digital Root 5

Name

Name	seven hundred one million seven hundred sixty-one thousand eight hundred ninety-five

Interesting facts

701761895 has 8 divisors, whose sum is 842359056
The reverse of 701761895 is 598167107
Previous prime number is 3793

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 44
Digital Root 8

Name

Name	nine hundred sixty-six million one hundred eighty-five thousand sixty-eight

Interesting facts

966185068 has 32 divisors, whose sum is 2201813280
The reverse of 966185068 is 860581669
Previous prime number is 89

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 49
Digital Root 4

Simplify sec(u)-tan(u)

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