Find Amplitude, Period, and Phase Shift f(x)=tan(x/2)

$f (x) = \tan (\frac{x}{2})$

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

$a = 1$

$b = \frac{1}{2}$

$c = 0$

$d = 0$

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

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

Period: $\frac{π}{| b |}$

Replace $b$ with $\frac{1}{2}$ in the formula for period.

Period: $\frac{π}{| \frac{1}{2} |}$

Solve the equation.

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$\frac{1}{2}$ is approximately $0.5$ which is positive so remove the absolute value

Period: $\frac{π}{\frac{1}{2}}$

Multiply the numerator by the reciprocal of the denominator.

Period: $π \cdot 2$

Move $2$ to the left of $π$ .

Period: $2 π$

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: $\frac{0}{\frac{1}{2}}$

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: $0 \cdot 2$

Multiply $0$ by $2$ .

Phase Shift: $0$

Find the vertical shift $d$ .

Vertical Shift: $0$

List the properties of the trigonometric function.

Amplitude: None

Period: $2 π$

Phase Shift: $0$ ( $0$ to the right)

Vertical Shift: $0$

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Name

Name	four hundred ninety-one million three hundred fifty-eight thousand four hundred ninety-five

Interesting facts

491358495 has 32 divisors, whose sum is 803639232
The reverse of 491358495 is 594853194
Previous prime number is 373

Basic properties

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

Name

Name	one billion nine hundred two million nine hundred forty-four thousand five hundred seventy-one

Interesting facts

1902944571 has 4 divisors, whose sum is 1960609592
The reverse of 1902944571 is 1754492091
Previous prime number is 33

Basic properties

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

Name

Name	eight hundred twenty-six million three hundred sixty-nine thousand one hundred ten

Interesting facts

826369110 has 64 divisors, whose sum is 2117016000
The reverse of 826369110 is 011963628
Previous prime number is 53

Basic properties

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

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

Factor f(x)=x^2+4x-32

Evaluate square root of 10368^2+17958^2

Find the Exact Value csc(405)

Convert to Trigonometric Form -8i