Trigonometry

Connect the unit circle to the sine, cosine and tangent graphs, solve basic trigonometric equations, and use elevation angles and the laws of sines and cosines to measure heights and distances.

7 interactive Mathematics simulations on trigonometry.

Trig identities – Pythagorean, compound angle, double angle and R cos(θ − α) Mathematics · Trigonometry Drag angles on the unit circle and on the stacked right-triangle diagram to verify sin²θ + cos²θ = 1, 1 + tan²θ =... Ages 16–17
Unit circle and the sine, cosine, tangent graphs Mathematics · Trigonometry Drag point M on the unit circle and the matching point moves in sync on the graph of y = sin x, cos x or tan x. The... Ages 16–17
Solving triangles – measuring a river's width with the Laws of Sines and Cosines Mathematics · Trigonometry Find the width of a river without crossing it: measure a baseline AB on one bank and the two angles to a tree C on... Ages 15–16
Bearings and navigation – journeys, return bearings, angles of elevation and depression Mathematics · Trigonometry Three-figure bearings measured clockwise from north, and back bearings (±180°). On the Journey screen a route of 1–3... Ages 15–16
Basic Trigonometric Equations on the Unit Circle Mathematics · Trigonometry Solve sin x = m, cos x = m, or tan x = m using the unit circle: the simulation marks the terminal points that... Ages 16–17
Trig ratios of an acute angle – measuring height with elevation angle Mathematics · Trigonometry Right triangle ABC, right-angled at A: drag vertex C to change the acute angle B = α, drag vertex A to change the... Ages 14–15
Unit circle – sine, cosine and tangent of any angle Mathematics · Trigonometry Drag point M around the unit circle (radius 1) to change the angle θ; the reference triangle and the tangent segment... Ages 16–17