Australian Curriculum Mathematics/Mathematical Methods/Trigonometric Functions

Australian Curriculum Content

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.