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.