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5.06 Transformations of sine and cosine

Interactive practice questions

Consider the two graphs:

$A$A: $y=\sin x$y=sinx

$B$B: $y=\sin x-2$y=sinx2.

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What vertical shift of $y=\sin x$y=sinx results in the graph of $y=\sin x-2$y=sinx2?

Translating the graph $3$3 units upwards.

A

Translating the graph $3$3 units downwards.

B

Translating the graph $2$2 units downwards.

C

Translating the graph $2$2 units upwards.

D
Easy
< 1min

Consider the two graphs:

$A$A: $y=\cos x$y=cosx

$B$B: $y=\cos x+2$y=cosx+2.

Easy
< 1min

Which of the following is the graph of $y=\sin x+3$y=sinx+3?

Easy
< 1min

The graph of $y=\sin x$y=sinx has been transformed into the graph of $y=\sin x-2$y=sinx2.

Easy
< 1min
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Outcomes

1.1.26

examine translations and the graphs of y=f(x)+a and y=f(x-b)

1.2.10

examine amplitude changes and the graphs of y=asin⁡x and y=acosx

1.2.11

examine period changes and the graphs of y=sin ⁡bx,y=cos bx, and y=tan ⁡bx

1.2.12

examine phase changes and the graphs of y=sin⁡(x-c), y=cos⁡(x-c) and y=tan⁡(x-c)

1.2.13

examine the relationships sin⁡(x+π/2)=cos⁡x and cos⁡(x−π/2)=sin⁡x

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