Trigonometric Graphs

New Zealand

Level 7 - NCEA Level 2

How does the graph of $y=3\cos x$`y`=3`c``o``s``x` differ from the graph of $y=\cos x$`y`=`c``o``s``x`?

Select the two correct options.

The amplitude of $y=3\cos x$`y`=3`c``o``s``x` is $3$3 times greater than the amplitude of $y=\cos x$`y`=`c``o``s``x`.

A

The period of $y=3\cos x$`y`=3`c``o``s``x` is greater than the period of $y=\cos x$`y`=`c``o``s``x`.

B

The maximum value of $y=3\cos x$`y`=3`c``o``s``x` is $3$3 times greater than the maximum value of $y=\cos x$`y`=`c``o``s``x`.

C

$y=3\cos x$`y`=3`c``o``s``x` is a reflection of $y=\cos x$`y`=`c``o``s``x` about the $x$`x`-axis.

D

Easy

Approx a minute

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

Determine the equation of the graphed function given that it is of the form $y=a\sin x$`y`=`a``s``i``n``x` or $y=a\cos x$`y`=`a``c``o``s``x`, 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`=`a``s``i``n``x` or $y=a\cos x$`y`=`a``c``o``s``x`, where $x$`x` is in degrees.

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