Explore trigonometric ratios, principal inverses, special-angle values and identities with a synchronized unit circle and discontinuity-aware graph.
01 / PURPOSE-SPECIFIC INPUTS
Exact special-angle labels require justified degree/symbolic inputs. Rounded numeric radians near poles are not silently treated as exact axes.
02 / RESULT & INTERACTIVE INSPECTION
This is a real trigonometric learning workspace, not a second general expression calculator. Right-triangle mode explains opposite/adjacent/hypotenuse ratios; use the existing Right Triangle Calculator for full dimensional solving. Inverse reciprocal functions, symbolic equation solving and arbitrary identity proof are unsupported.
θ=30°; reference 30°; quadrant I. sin=0.5, cos=0.866, tan=0.5774. Justified special-angle forms are shown in the main result.
| Function | Relationship | Selected value |
|---|---|---|
| sin | opposite / hypotenuse | 1/2 ≈ 0.5 |
| cos | adjacent / hypotenuse | √3/2 ≈ 0.8660254 |
| tan | opposite / adjacent | √3/3 ≈ 0.57735027 |
| csc | hypotenuse / opposite | ≈ 2 |
| sec | hypotenuse / adjacent | ≈ 1.15470054 |
| cot | adjacent / opposite | ≈ 1.73205081 |
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Review the explanation, copy supported outputs or reset the workspace.
It focuses on unit-circle coordinates, reference angles, quadrant signs, ratios, principal inverses and a synchronized graph. It is not a second general scientific expression calculator or dimensional right-triangle solver.
Explore trigonometric ratios, principal inverses, special-angle values and identities with a synchronized unit circle and discontinuity-aware graph. Inspect real calculated values through accessible visual controls and review the worked assumptions.
Trigonometry Calculator calculates locally in browser memory. Financial values, schedules, measurements, health inputs and other entries are not sent to a third-party calculation-processing API or stored as a personal profile. Ordinary page requests may still be logged. Clipboard access occurs only when you choose Copy Result.
It focuses on unit-circle coordinates, reference angles, quadrant signs, ratios, principal inverses and a synchronized graph. It is not a second general scientific expression calculator or dimensional right-triangle solver.
Justified degree inputs and recognized symbolic pi-based radian inputs can receive rational/radical forms such as sin30°=1/2. Rounded numeric radian inputs near axes are not automatically promoted to exact symbolic values.
Tangent and secant are undefined where cosine is zero, including exact 90 degrees. Cosecant and cotangent are undefined where sine is zero. These cases are labeled rather than divided by an approximate zero.
Arcsine returns −90 through 90 degrees, arccosine zero through 180, and arctangent strictly between −90 and 90. These principal values are not the full periodic solution set of a trigonometric equation.
The graph explicitly omits tangent poles, breaks its SVG path across them and omits magnitudes outside the stated vertical range. It never draws one continuous segment through a vertical asymptote.
Yes. The angle range input and the focusable circle’s arrow-key controls recalculate the main answer. Pointer dragging is also supported. The sin²+cos² display illustrates a known identity without claiming to prove arbitrary symbolic equalities.