Trigonometry Examples

$y = \tan (π x)$

Step 1

Use the form

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

$a = 1$

$b = π$

$c = 0$

$d = 0$

Step 2

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

Step 3

Find the period of

$\tan (π x)$ .

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Step 3.1

The period of the function can be calculated using

$\frac{π}{| b |}$ .

$\frac{π}{| b |}$

Step 3.2

Replace

$b$ with

$π$ in the formula for period.

$\frac{π}{| π |}$

Step 3.3

$π$ is approximately

$3.14159265$ which is positive so remove the absolute value

$\frac{π}{π}$

Step 3.4

Cancel the common factor of

$π$ .

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Step 3.4.1

Cancel the common factor.

$\frac{π}{π}$

Step 3.4.2

Rewrite the expression.

$1$

Step 4

Find the phase shift using the formula

$\frac{c}{b}$ .

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Step 4.1

The phase shift of the function can be calculated from

$\frac{c}{b}$ .

Phase Shift:

$\frac{c}{b}$

Step 4.2

Replace the values of

$c$ and

$b$ in the equation for phase shift.

Phase Shift:

$\frac{0}{π}$

Step 4.3

Divide

$0$ by

$π$ .

Phase Shift:

$0$

Phase Shift:

$0$

Step 5

List the properties of the trigonometric function.

Amplitude: None

Period:

$1$

Phase Shift: None

Vertical Shift: None

Step 6