7. Trigonometry
iGCSE (2021 Edition)
7.11 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.
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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$0≤x<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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