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AustraliaVIC
VCE 11 Methods 2023

8.06 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.

Loading Graph...

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

U1.AoS1.7

the effect of transformations of the plane, dilation, reflection in axes, translation and simple combinations of these transformations, on the graphs of functions

U1.AoS1.13

describe the effect of transformations on the graphs of relations and functions

U1.AoS2.9

representations of points and transformations

U1.AoS2.5

transformations of the plane and application to basic functions and relations by simple combinations of dilations (students should be familiar with both ‘parallel to an axis’ and ‘from an axis’ descriptions), reflections in an axis and translations (matrix representation may be used but is not required)

U2.AoS1.19

sketch by hand the unit circle, graphs of the sine, cosine and exponential functions, and simple transformations of these to the form Af(bx)+c , sketch by hand graphs of log_a(x) and the tangent function, and identify any vertical or horizontal asymptotes

U2.AoS1.5

circular functions of the form y=Af(nx)+c and their graphs, where f is the sine, cosine or tangent function

U2.AoS1.15

the effect of transformations of the plane on the graphs of sine, cosine, tangent and exponential functions

U2.AoS1.21

describe the effect of transformations of the plane on the graphs of the sine, cosine, tangent and exponential functions

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