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New Zealand
Level 7 - NCEA Level 2

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 Cartesian coordinate system with the x-axis ranging from 0 to $420$420 degrees in major intervals of 120, and minor intervals of $60$60 and the y-axis labeled from 1 to $-4$4 in intervals of $0.5$0.5. Two functions are plotted: the function $f\left(x\right)$f(x) in gray, and $g\left(x\right)=f\left(x-k\right)-j$g(x)=f(xk)j in black. The two curves appear to be identical periodic oscillations. The black curve is located below the gray curve. The peaks of the black curve is located units below and to the right of where the peaks occur on the gray curve.
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
b

Determine the value of $j$j.

c

Determine the smallest positive value of $k$k.

Easy
1min

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))).

Easy
1min

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

Easy
< 1min

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.

Easy
1min
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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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