Trigonometry

Trigonometry | NSW Curriculum Website

MST-12-S2-04 applies trigonometry to solve problems involving right-angled and non-right-angled triangles

📖 Prior Knowledge

Content	Prior knowledge	Used for
Right-angled Triangles	- Pythagoras’ theorem	- solving trigonometry problems
Trigonometry A	- trig ratios	- repeated content
Trigonometry B	- angle of elevation/depression, bearings	- repeated content
Trigonometry C	- sine rule, cosine rule, sine rule for area	- repeated content

Apply trigonometric ratios to right-angled triangles to find either the lengths of unknown sides or the size of unknown angles in both degrees, and degrees and minutes
Apply the sine rule $\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$ in a given triangle $A B C$ to find the value of an unknown side
Apply the sine rule $\frac{sin A}{a} = \frac{sin B}{b} = \frac{sin C}{c}$ in a given triangle $A B C$ to find the value of an unknown angle, excluding the ambiguous case
Apply the sine rule in a given triangle to find the value of an unknown angle, given that the unknown angle is obtuse
Apply the cosine rule $c^{2} = a^{2} + b^{2} - 2 ab cos C$ in a given triangle $A B C$ to find the value of an unknown side
Apply the cosine rule $cos C = \frac{a ^{2} + b ^{2} - c ^{2}}{2 ab}$ in a given triangle ABC to find the value of an unknown angle
Apply the formula $A = \frac{1}{2} ab sin C$ , where $a$ and $b$ are the sides that form the included angle $C$ in a given triangle $A B C$ , to solve problems in a range of contexts
Identify and interpret true bearings and compass bearings and convert between them
Construct and interpret compass radial surveys and solve related problems
Solve practical problems involving Pythagoras’ theorem, the trigonometry of right-angled and non-right-angled triangles, angles of elevation and depression, and true bearings and compass bearings