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	Prerequisite relationships
Angle Relationships	- Find unknown angles with parallel lines → Find the bearing between two points
Trigonometry A	- Find an angle from a trig ratio → Find an unknown angle using trigonometry - Evaluate a trigonometric ratio → Find an unknown side using trigonometry - Find an unknown side using trigonometry (revisited content) - Find an unknown side in the denominator → Solve practical trigonometry problems - Find an unknown angle using trigonometry (revisited content) - Round an angle to the nearest degree or minute → Find an unknown angle using trigonometry - Solve practical trigonometry problems (revisited content)
Trigonometry B	- Identify an angle of elevation or depression → Solve elevation and depression problems - Solve elevation and depression problems (revisited content) - Interpret and convert bearings (revisited content) - Find the bearing between two points (revisited content) - Solve bearings problems (revisited content)
Trigonometry C	- Label the sides and angles of a triangle → Apply the sine rule - Label the sides and angles of a triangle → Apply the cosine rule - Apply the sine rule (revisited content) - Apply the sine rule to find an angle (revisited content) - Apply the cosine rule (revisited content) - Apply the cosine rule to find an angle (revisited content) - Apply the area rule for triangles (revisited content) - Solve non-right-angled triangle problems (revisited 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