Match each trigonometric function on the left with its correct combination of amplitude an… — ACT

Match each trigonometric function on the left with its correct combination of amplitude and period on the right.

f(x) = 4 \sin(3x)

matches Amplitude = 4, Period =

\frac{2\pi}{3}

;

g(x) = 2 \cos\left(\frac{1}{2}x\right)

matches Amplitude = 2, Period =

4\pi

;

h(x) = -3 \sin(2x)

matches Amplitude = 3, Period =

\pi

Each trigonometric function is correctly evaluated using the general properties: Amplitude equals

|A|

and Period equals

\frac{2\pi}{|B|}

Identify the standard trigonometric form parameters.

For equations of the form

y = A \sin(Bx)

y = A \cos(Bx)

, Amplitude

= |A|

and Period

= \frac{2\pi}{|B|}

Applying the definitions of amplitude and period for sine and cosine functions.

Calculate amplitude and period for

f(x) = 4 \sin(3x)

Amplitude

= |4| = 4

, Period

= \frac{2\pi}{3}

Here

A = 4

and

B = 3

Calculate amplitude and period for

g(x) = 2 \cos\left(\frac{1}{2}x\right)

Amplitude

= |2| = 2

, Period

= \frac{2\pi}{1/2} = 4\pi

Here

A = 2

and

B = \frac{1}{2}

Calculate amplitude and period for

h(x) = -3 \sin(2x)

Amplitude

= |-3| = 3

, Period

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

Here

A = -3

(so

|A| = 3

) and

B = 2

Amplitude and Period of Sine and Cosine Graphs

Question