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7.06 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=sinxβˆ’2.

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

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=sinxβˆ’2.

Easy
< 1min
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Outcomes

1.2.1.4

examine transformations of the graphs of 𝑓(π‘₯), including dilations and reflections, and the graphs of 𝑦=π‘Žf(π‘₯) and 𝑦=𝑓(𝑏x), translations, and the graphs of 𝑦=𝑓(π‘₯+𝑐) and 𝑦=𝑓(π‘₯)+𝑑; π‘Ž,𝑏,𝑐,𝑑 ∈ R

2.3.2.4

investigate the effect of the parameters 𝐴,𝐡,𝐢 and 𝐷 on the graphs of 𝑦=𝐴sin(𝐡(π‘₯+𝐢))+𝐷, 𝑦=𝐴cos(𝐡(π‘₯+𝐢))+𝐷 with and without technology

2.3.2.5

sketch the graphs of 𝑦=𝐴sin(𝐡(π‘₯+𝐢))+𝐷, 𝑦=𝐴cos(𝐡(π‘₯+𝐢))+𝐷 with and without technology

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