Trigonometry studies the relationships between angles and sides of triangles, and extends these ideas into functions that model periodic phenomena.

Key Topics

• Right Triangle Trigonometry — Sine, cosine, and tangent as ratios of sides.
• The Unit Circle — Defining trig functions for all angles using the circle of radius 1.
• Trigonometric Functions — \(\sin(\theta)\), \(\cos(\theta)\), \(\tan(\theta)\) and their reciprocals.
• Graphs of Trig Functions — Amplitude, period, phase shift, and vertical shift.
• Trigonometric Identities — Pythagorean, double-angle, sum/difference, and half-angle identities.
• Law of Sines and Cosines — Solving oblique (non-right) triangles.
• Inverse Trig Functions — \(\arcsin(x)\), \(\arccos(x)\), \(\arctan(x)\).
• Polar Coordinates — Representing points and curves using \((r, \theta)\).

Why It Matters

Trigonometry is essential in physics (waves, oscillations, sound), engineering (signal processing), astronomy (orbital mechanics), and computer graphics (rotations and animations).