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ACMMM027

recognise the distinction between functions and relations, and the vertical line test.

ACMMM028

review sine, cosine and tangent as ratios of side lengths in right-angled triangles

ACMMM029

understand the unit circle definition of \(\cos\theta,\;\sin\theta\) and \(\tan\theta\) and periodicity using degrees

ACMMM030

examine the relationship between the angle of inclination of a line and the gradient of that line

ACMMM031

establish and use the sine and cosine rules and the formula \(Area=\frac12bc\sin A\) for the area of a triangle.

ACMMM032

define and use radian measure and understand its relationship with degree measure

ACMMM033

calculate lengths of arcs and areas of sectors in circles.

ACMMM034

understand the unit circle definition of \(\cos\theta,\;\sin\theta\) and \(\tan\theta\) and periodicity using radians

ACMMM035

recognise the exact values of \(\cos\theta,\;\sin\theta\) and \(\tan\theta\) at integer multiples of \(\frac\pi6\) and \(\frac\pi4\)

ACMMM036

recognise the graphs of \(y=\sin x,\;y=\cos x,\) and \(y=\tan x\) on extended domains

ACMMM037

examine amplitude changes and the graphs of \(y=a\sin x\) and \(y=a\cos x\)

ACMMM038

examine period changes and the graphs of \(y=\sin bx,\;\), \(y=\cos bx\), and \(y=\tan bx\)

examine phase changes and the graphs of \(y=\sin{(x+c)}\), \(y=\cos{(x+c)}\) and \(y=\tan{(x+c)}\) and the relationships \(\sin\left(x+\frac\pi2\right)=\cos x\) and \(\cos\left(x-\frac\pi2\right)=\sin x\)

ACMMM041

prove and apply the angle sum and difference identities

ACMMM042

identify contexts suitable for modelling by trigonometric functions and use them to solve practical problems

ACMMM043

solve equations involving trigonometric functions using technology, and algebraically in simple cases.

ACMMM044

understand the notion of a combination as an unordered set of \(r\) objects taken from a set of \(n\) distinct objects

ACMMM045

use the notation \(\begin{pmatrix}n\\r\end{pmatrix}\) and the formula \(\begin{pmatrix}n\\r\end{pmatrix}=\frac{n!}{r!\left(n-r\right)!}\) for the number of combinations of \(r\) objects taken from a set of \(n\) distinct objects

ACMMM046

expand \(\left(x+y\right)^n\) for small positive integers \(n\)

ACMMM047

recognise the numbers \(\begin{pmatrix}n\\r\end{pmatrix}\) as binomial coefficients, (as coefficients in the expansion of \(\left(x+y\right)^n)\)

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