Mathematics K–10 - Stage 5 - Trigonometry C (Path) | NSW Curriculum

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Trigonometry C (Path)

MAO-WM-01
develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly
MA5-TRG-P-01
applies Pythagoras’ theorem and trigonometry to solve 3-dimensional problems and applies the sine, cosine and area rules to solve 2-dimensional problems, including bearings (Path: Stn, Adv)

Trigonometry C (Path)

Stn (Standard), Adv (Advanced) and Ext (Extension) have been used to suggest paths for related Stage 6 courses.

Solve 3-dimensional problems involving right-angled triangles

Apply Loading to solve problems involving the Loading of the Loading and diagonals of Loading prisms and other 3-dimensional Loading
Apply trigonometry to solve problems involving right-angled Loading in 3 dimensions, including using Loading and Loading and Loading

Apply the sine, cosine and area rules to any triangle and solve related problems

Use graphing applications to verify the sine rule $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$ and that the ratios of a side to the sine of the opposite angle is a constant
Apply the sine rule in a given triangle $A B C$ to find the value of an unknown side
Apply the sine rule in a given triangle $A B C$ to find the value of an unknown angle (ambiguous case excluded): $\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$
Use graphing applications to verify the cosine rule $c^{2} = a^{2} + b^{2} - 2 a b \cos C$ .
Apply the cosine rule to find the unknown sides for a given triangle $A B C$ .
Rearrange the formula to deduce that $\cos C = \frac{a^{2} + b^{2} - c^{2}}{2 a b}$ and use this to find an unknown angle
Use graphing applications to verify the area rule $A = \frac{1}{2} a b \sin C$ .
Apply the formula $A = \frac{1}{2} a b \sin C$ , where $a$ and $b$ are the sides that form angle $C$ to find the area of a given triangle $A B C$
Solve problems involving finding unknown Loading or Loading in triangles (excluding right-angled triangles) by selecting and applying the appropriate rule

Related files

Life Skills

K–10Mathematics K–10 Syllabus (2022)