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Standard Level

6.01 Amplitude, vertical shifts and dilations of trigonometric graphs

Interactive practice questions

Consider the expression $\cos\theta$cosθ.

a

Complete the table of values for different values of $\theta$θ.

$\theta$θ $0$0 $\frac{\pi}{3}$π3 $\frac{\pi}{2}$π2 $\frac{2\pi}{3}$2π3 $\pi$π $\frac{4\pi}{3}$4π3 $\frac{3\pi}{2}$3π2 $\frac{5\pi}{3}$5π3 $2\pi$2π
$\cos\theta$cosθ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
b

Graph the function $y=\cos\theta$y=cosθ.

Loading Graph...
c

What is the largest possible value of $\cos\theta$cosθ?

d

What is the smallest possible value of $\cos\theta$cosθ?

e

What is the range of values of $4\cos\theta$4cosθ?

$\editable{}\le4\cos\theta\le\editable{}$4cosθ

Easy
6min

Consider the graph of the function of the form $f\left(x\right)=A\sin x$f(x)=Asinx.

Easy
< 1min

Determine the equation of the graphed function given that it is of the form $y=a\sin x$y=asinx or $y=a\cos x$y=acosx.

Easy
< 1min

Consider the graph of $y=\sin x$y=sinx for $0\le x<2\pi$0x<2π.

At which value of $x$x in the given domain would $y=-\sin x$y=sinx have a maximum value?

Easy
1min
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