Trigonometry Examples

y = - 5 tan (3 x + π)

$y = - 5 \tan (3 x + π)$

Step 1

Use the form

a tan (b x - c) + d

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

a = - 5

$a = - 5$

b = 3

$b = 3$

c = - π

$c = - π$

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

- 5 tan (3 x + π)

$- 5 \tan (3 x + π)$ .

Tap for more steps...

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

3

$3$ in the formula for period.

\frac{π}{| 3 |}

$\frac{π}{| 3 |}$

Step 3.3

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

0

$0$ and

3

$3$ is

3

$3$ .

\frac{π}{3}

$\frac{π}{3}$

\frac{π}{3}

$\frac{π}{3}$

Step 4

Find the phase shift using the formula

\frac{c}{b}

$\frac{c}{b}$ .

Tap for more steps...

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{- π}{3}

$\frac{- π}{3}$

Step 4.3

Move the negative in front of the fraction.

Phase Shift:

- \frac{π}{3}

$- \frac{π}{3}$

Phase Shift:

- \frac{π}{3}

$- \frac{π}{3}$

Step 5

List the properties of the trigonometric function.

Amplitude: None

Period:

\frac{π}{3}

$\frac{π}{3}$

Phase Shift:

- \frac{π}{3}

$- \frac{π}{3}$ (

\frac{π}{3}

$\frac{π}{3}$ to the left)

Vertical Shift: None

Step 6