Trigonometry Examples

y = 3 sin (2 x)

$y = 3 \sin (2 x)$

Step 1

Use the form

a sin (b x - c) + d

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

a = 3

$a = 3$

b = 2

$b = 2$

c = 0

$c = 0$

d = 0

$d = 0$

Step 2

Find the amplitude

| a |

$| a |$ .

Amplitude:

3

$3$

Step 3

Find the period of

3 sin (2 x)

$3 \sin (2 x)$ .

Tap for more steps...

Step 3.1

The period of the function can be calculated using

\frac{2 π}{| b |}

$\frac{2 π}{| b |}$ .

\frac{2 π}{| b |}

$\frac{2 π}{| b |}$

Step 3.2

Replace

b

$b$ with

2

$2$ in the formula for period.

\frac{2 π}{| 2 |}

$\frac{2 π}{| 2 |}$

Step 3.3

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

0

$0$ and

2

$2$ is

2

$2$ .

\frac{2 π}{2}

$\frac{2 π}{2}$

Step 3.4

Cancel the common factor of

2

$2$ .

Tap for more steps...

Step 3.4.1

Cancel the common factor.

$\frac{2 π}{2}$

Step 3.4.2

Divide

$π$ by

$1$ .

$π$

Step 4

Find the phase shift using the formula

$\frac{c}{b}$ .

Tap for more steps...

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:

$\frac{0}{2}$

Step 4.3

Divide

$0$ by

$2$ .

Phase Shift:

$0$

Phase Shift:

$0$

Step 5

List the properties of the trigonometric function.

Amplitude:

$3$

Period:

$π$

Phase Shift: None

Vertical Shift: None

Step 6

$y = 3 \sin 2 x$

(

)

[

]

√



≥















≤



































