Consider the expression $\cos\theta$cosθ.
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 | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
Graph the function $y=\cos\theta$y=cosθ.
What is the largest possible value of $\cos\theta$cosθ?
What is the smallest possible value of $\cos\theta$cosθ?
What is the range of values of $4\cos\theta$4cosθ?
$\editable{}\le4\cos\theta\le\editable{}$≤4cosθ≤
Consider the graph of the function of the form $f\left(x\right)=A\sin x$f(x)=Asinx.
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.
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?
Understand the relationship between y = f(x) and y = |f(x)|, where f(x) may be linear, quadratic or trigonometric.
Understand amplitude and periodicity and the relationship between graphs of related trigonometric functions, e.g. sin x and sin 2x.
Draw and use the graphs of y = asinbx + c, y = acos bx + c, y = atan bx + c where a is a positive integer, b is a simple fraction or integer (fractions will have a denominator of 2, 3, 4, 6 or 8 only), and c is an integer.