NZ Level 7 (NZC) Level 2 (NCEA)
Amplitude of sine and cosine

## Interactive practice questions

How does the graph of $y=3\cos x$y=3cosx differ from the graph of $y=\cos x$y=cosx?

Select all the correct options.

The amplitude of $y=3\cos x$y=3cosx is $3$3 times greater than the amplitude of $y=\cos x$y=cosx.

A

The period of $y=3\cos x$y=3cosx is greater than the period of $y=\cos x$y=cosx.

B

The maximum value of $y=3\cos x$y=3cosx is $3$3 times greater than the maximum value of $y=\cos x$y=cosx.

C

$y=3\cos x$y=3cosx is a reflection of $y=\cos x$y=cosx about the $x$x-axis.

D

The amplitude of $y=3\cos x$y=3cosx is $3$3 times greater than the amplitude of $y=\cos x$y=cosx.

A

The period of $y=3\cos x$y=3cosx is greater than the period of $y=\cos x$y=cosx.

B

The maximum value of $y=3\cos x$y=3cosx is $3$3 times greater than the maximum value of $y=\cos x$y=cosx.

C

$y=3\cos x$y=3cosx is a reflection of $y=\cos x$y=cosx about the $x$x-axis.

D
Easy
Approx a minute

Consider the graph of $y=\cos x$y=cosx, shown below. Use the characteristics of this graph to state the amplitude of $y=4\cos x$y=4cosx.

Determine the equation of the graphed function given that it is of the form $y=a\sin x$y=asinx or $y=a\cos x$y=acosx, where $x$x is in degrees.

Determine the equation of the graphed function given that it is of the form $y=a\sin x$y=asinx or $y=a\cos x$y=acosx, where $x$x is in degrees.

### Outcomes

#### M7-2

Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs

#### 91257

Apply graphical methods in solving problems