Trigonometry Examples

f (t) = - 7 \tan (4 t)

$f (t) = - 7 \tan (4 t)$

Step 1

Use the form

a \tan (b t - c) + d

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

a = - 7

$a = - 7$

b = 4

$b = 4$

c = 0

$c = 0$

d = 0

$d = 0$

Step 2

Since the graph of the function

t a n

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

Amplitude: None

Step 3

Find the period of

- 7 \tan (4 t)

$- 7 \tan (4 t)$ .

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Step 3.1

The period of the function can be calculated using

\frac{π}{| b |}

$\frac{π}{| b |}$ .

\frac{π}{| b |}

$\frac{π}{| b |}$

Step 3.2

Replace

b

$b$ with

4

$4$ in the formula for period.

\frac{π}{| 4 |}

$\frac{π}{| 4 |}$

Step 3.3

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

0

$0$ and

4

$4$ is

4

$4$ .

\frac{π}{4}

$\frac{π}{4}$

\frac{π}{4}

$\frac{π}{4}$

Step 4

Find the phase shift using the formula

\frac{c}{b}

$\frac{c}{b}$ .

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Step 4.1

The phase shift of the function can be calculated from

\frac{c}{b}

$\frac{c}{b}$ .

Phase Shift:

\frac{c}{b}

$\frac{c}{b}$

Step 4.2

Replace the values of

c

$c$ and

b

$b$ in the equation for phase shift.

Phase Shift:

\frac{0}{4}

$\frac{0}{4}$

Step 4.3

Divide

0

$0$ by

4

$4$ .

Phase Shift:

0

$0$

Phase Shift:

0

$0$

Step 5

List the properties of the trigonometric function.

Amplitude: None

Period:

\frac{π}{4}

$\frac{π}{4}$

Phase Shift: None

Vertical Shift: None

Step 6