Australian Curriculum Mathematics/Mathematical Methods/Trigonometric Functions

Australian Curriculum ContentSource: Australian Curriculum, Assessment and Reporting Authority (ACARA), downloaded from the Australian Curriculum website on (5 October 2015). Cosine and sine rules review sine, cosine and tangent as ratios of side lengths in right-angled triangles understand the unit circle definition of cosθ, sinθ and tanθ and periodicity using degrees examine the relationship between the angle of inclination of a line and the gradient of that line establish and use the sine and cosine rules and the formula Area=12bcsinA for the area of a triangle. Circular measure and radian measure define and use radian measure and understand its relationship with degree measure calculate lengths of arcs and areas of sectors in circles. Trigonometric functions understand the unit circle definition of cosθ, sinθ and tanθ and periodicity using radians recognise the exact values of sinθ, cosθ and tanθ at integer multiples of π6 and π4 recognise the graphs of y=sinx, y=cosx, and y=tanx on extended domains examine amplitude changes and the graphs of y=asinx and y=acosx examine period changes and the graphs of y=sinbx, y=cosbx, 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(x+π2)=cosx and cos(x−π2)=sinx prove and apply the angle sum and difference identities identify contexts suitable for modelling by trigonometric functions and use them to solve practical problems solve equations involving trigonometric functions using technology, and algebraically in simple cases. __TOC__ References