NZ Level 7 (NZC) Level 2 (NCEA)
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Transformations of sine and cosine curves and equations

Interactive practice questions

The graph of $f\left(x\right)$f(x) and $g\left(x\right)=f\left(x-k\right)-j$g(x)=f(xk)j are displayed on the same set of axes in grey and black respectively.

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a

What transformations have occurred from $f\left(x\right)$f(x) to $g\left(x\right)$g(x)? Select all that apply.

Vertical translation of $60$60 units up.

A

Horizontal translation of $3^\circ$3° left.

B

Horizontal translation of $60^\circ$60° right.

C

Vertical translation of $3$3 units down.

D

Vertical translation of $60$60 units up.

A

Horizontal translation of $3^\circ$3° left.

B

Horizontal translation of $60^\circ$60° right.

C

Vertical translation of $3$3 units down.

D
b

Determine the value of $j$j.

c

Determine the smallest positive value of $k$k.

Easy
Approx 2 minutes
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Consider the graphs of $y=\sin x$y=sinx and $y=5\sin\left(x+\left(\left(-60\right)\right)\right)$y=5sin(x+((60))).

Consider the graphs of $y=\cos x$y=cosx and $y=2\cos\left(x+45^\circ\right)$y=2cos(x+45°).

The graph of $y=\sin x$y=sinx has been transformed into the graph of $y=\sin\left(x+\left(\left(-45\right)\right)\right)-2$y=sin(x+((45)))2.

Outcomes

M7-2

Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs

91257

Apply graphical methods in solving problems

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