Trigonometric Graphs

NZ Level 7 (NZC) Level 2 (NCEA)

Amplitude of sine and cosine

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 all the 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

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

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