Match each of the trigonometric functions listed on the left with the correct description … — ACT

Match each of the trigonometric functions listed on the left with the correct description of its amplitude and period listed on the right.

The function

y = 3\sin(2x)

matches the description stating 'Amplitude is 3 and period is

\pi

'. The function

y = 2\cos(3x)

matches the description stating 'Amplitude is 2 and period is

\frac{2\pi}{3}

'. The function

y = 4\sin(\pi x)

matches the description stating 'Amplitude is 4 and period is 2'.

Each trigonometric function of the form

y = a\sin(bx)

y = a\cos(bx)

has an amplitude equal to the absolute value of the coefficient of the trigonometric term (

|a|

) and a period equal to

2\pi

divided by the absolute value of the coefficient of the angle variable (

|b|

). Applying these formulas gives the correct properties for each function.

Identify the general form of the trigonometric functions

The functions are in the form

y = a\sin(bx)

y = a\cos(bx)

, where the amplitude is given by the absolute value of the vertical stretch coefficient (

|a|

), and the period is calculated as

\frac{2\pi}{|b|}

This establishes the formulas needed to determine the amplitude and period for each equation.

Calculate the properties for

y = 3\sin(2x)

The vertical stretch coefficient is 3, so the amplitude is 3. The frequency coefficient is 2, so the period is

\frac{2\pi}{2} = \pi

To find the amplitude and period for the first function.

Calculate the properties for

y = 2\cos(3x)

The vertical stretch coefficient is 2, so the amplitude is 2. The frequency coefficient is 3, so the period is

\frac{2\pi}{3}

To find the amplitude and period for the second function.

Calculate the properties for

y = 4\sin(\pi x)

The vertical stretch coefficient is 4, so the amplitude is 4. The frequency coefficient is

\pi

, so the period is

\frac{2\pi}{\pi} = 2

To find the amplitude and period for the third function.

Identifying the amplitude and calculating the period of trigonometric functions from their equations

Estimated Time:1m 30s

Question