 New Zealand
Level 7 - NCEA Level 2

# Phase shifts for sine and cosine

## Interactive practice questions

Consider the given graph of $y=\cos\left(x+180^\circ\right)$y=cos(x+180°).

a

What is the amplitude of the function?

b

How can the graph of $y=\cos x$y=cosx be transformed into the graph of $y=\cos\left(x+180^\circ\right)$y=cos(x+180°)?

By reflecting it about the $x$x-axis, and then translating it horizontally $180$180 units to the left.

A

By translating it horizontally $180$180 units to the right.

B

By translating it horizontally $180$180 units to the left.

C

By changing the period of the function.

D

By reflecting it about the $x$x-axis, and then translating it horizontally $180$180 units to the right.

E
Easy
Less than a minute

Consider the function $f\left(x\right)=\sin x$f(x)=sinx and $g\left(x\right)=\sin\left(x-90^\circ\right)$g(x)=sin(x90°).

Consider the function $f\left(x\right)=\cos x$f(x)=cosx and $g\left(x\right)=\cos\left(x-90^\circ\right)$g(x)=cos(x90°).

The functions $f\left(x\right)$f(x) and $g\left(x\right)=f\left(x+k\right)$g(x)=f(x+k) have been graphed on the same set of axes in grey and black respectively.

### 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