New Zealand
Level 8 - NCEA Level 3

# Phase shifts for sine and cosine

## Interactive practice questions

Consider the given graph of $y=\cos\left(x+\frac{\pi}{2}\right)$y=cos(x+π2).

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 $y=\cos\left(x+\frac{\pi}{2}\right)$y=cos(x+π2)?

By reflecting it about the $x$x-axis, and then translating it horizontally $\frac{\pi}{2}$π2 units to the left.

A

By reflecting it about the $x$x-axis, and then translating it horizontally $\frac{\pi}{2}$π2 units to the right.

B

By translating it horizontally $\frac{\pi}{2}$π2 units to the right.

C

By changing the period of the function.

D

By translating it horizontally $\frac{\pi}{2}$π2 units to the left.

E

By reflecting it about the $x$x-axis, and then translating it horizontally $\frac{\pi}{2}$π2 units to the left.

A

By reflecting it about the $x$x-axis, and then translating it horizontally $\frac{\pi}{2}$π2 units to the right.

B

By translating it horizontally $\frac{\pi}{2}$π2 units to the right.

C

By changing the period of the function.

D

By translating it horizontally $\frac{\pi}{2}$π2 units to the left.

E
Easy
Less than a minute

Consider the function $f\left(x\right)=\sin x$f(x)=sinx and $g\left(x\right)=\sin\left(x-\frac{\pi}{2}\right)$g(x)=sin(xπ2).

Consider the function $f\left(x\right)=\cos x$f(x)=cosx and $g\left(x\right)=\cos\left(x-\frac{\pi}{2}\right)$g(x)=cos(xπ2).

Consider the function $y=\sin\left(x-\frac{\pi}{2}\right)$y=sin(xπ2).

### Outcomes

#### M8-2

Display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions