Trigonometry Visual Tools

An interactive angle visualizer that lets you set any angle in degrees or radians and instantly see its type, quadrant, reference angle, and its complementary, supplementary, and coterminal partners. Toggle reference lines, jump to preset unit-circle angles, and read live values for sin, cos, tan, csc, sec, and cot, including exact special-angle forms.

An interactive hub for nine core angle concepts in trigonometry. Drag handles or use presets to explore basic classifications (acute, right, obtuse, straight, reflex), pairwise relationships (complementary, supplementary, vertical, adjacent), and trigonometric foundations (standard position, reference angles, coterminal angles, the 16 special unit-circle angles, and directed angles with even and odd verification).

Drag the blue dot around the unit circle to watch sine, cosine, tangent, and their reciprocals emerge as signed legs and ratios. Switch between the six functions via tabs, step through a five-stage derivation for each, and use the multi-turn slider to explore periodicity and coterminal angles.

Double-Angle identities explorer covering all six trigonometric functions. Animated geometric proofs derive sin(2θ) and cos(2θ) from a bisected isosceles triangle, while algebraic derivation cards handle tan(2θ), csc(2θ), sec(2θ), and cot(2θ) with one-click jumps back to their source proofs. A live formula table and verification cards confirm each identity numerically as you sweep the angle.

Half-Angle identities explorer covering all six trigonometric functions. Animated geometric proofs derive sin(α/2) and cos(α/2) from a bisected isosceles triangle, while algebraic derivation cards handle tan(α/2), csc(α/2), sec(α/2), and cot(α/2) with one-click jumps back to their source proofs. A live formula table and verification cards confirm each identity numerically as you sweep α from 20° to 160°.

Negative-Angle identities explorer covering all six trigonometric functions. Animated reflection proofs derive sin(-θ) = -sin θ and cos(-θ) = cos θ from a point and its mirror image across the x-axis on the unit circle, while algebraic derivation cards handle tan, csc, sec, and cot. A live formula table and verification cards label each function

Pythagorean identities explorer covering all six trigonometric functions. The base identity sin²θ + cos²θ = 1 is proved geometrically inside the unit circle, then tan, csc, sec, and cot forms follow by dividing through and rearranging. Animated steps, algebraic derivation cards with jump-to-source buttons, and a live formula table verify every identity numerically as you sweep θ through the first quadrant.

Explore all six trig functions at π − θ across two complementary views. Sin and cos appear as reflections across the y-axis with live unit-circle geometry; tan, csc, sec, and cot derive algebraically from those two roots. Step through proofs, switch tabs, and verify each identity numerically at any angle.

An interactive trigonometric functions visualizer that graphs sine, cosine, tangent, cosecant, secant, and cotangent in real time. Switch between degrees and radians, drag the angle slider through a full rotation, jump to special-angle presets, and watch live function values, periods, ranges, and asymptotes update on the plot and in the explanation panel.

An interactive quadrant explorer that shows the sign of every trigonometric function in each of the four quadrants. Click a quadrant or press 1-4, pick a function, and watch the unit circle, coordinate signs, ASTC rule, and step-by-step reasoning update together. A clean way to internalize why sine, cosine, tangent, and their reciprocals flip sign as the angle moves around the circle.

An interactive triangle visualizer with twelve preloaded scenarios covering classifications (equilateral, isosceles, acute, obtuse, right scalene), special right triangles (45-45-90, 30-60-90, 3-4-5, 5-12-13), and the laws of sines and cosines. Drag vertices, lock up to two angles, zoom freely, and read live stats and context-aware explanations including Pythagoras, SOH CAH TOA, and the trigonometric laws.