EVALUATE · INVERT · VISUALIZE
Trigonometry Calculator
Go from an angle to all six trig functions, from a ratio back to angles, or solve a right triangle. Exact special-angle values and unit-circle context stay beside the decimal answer.
6 functionssin through cot
exactspecial angles
localno upload
TRIG WORKBENCH
Choose the direction of the problem
ANGLE LAB
Evaluate one angle completely
Radians accept π forms such as pi/6, 3pi/4 and -7π/6.
INVERSE TRIG
Find the angle from a ratio
arcsin/arccos require −1 ≤ x ≤ 1. Results show the principal value and all matching angles from 0° to <360°.
PRINCIPAL VALUE30°
π/6 radians
SOLUTIONS IN 0° ≤ θ < 360°30°, 150°
SOHCAHTOA RIGHT TRIANGLE
Enter exactly two known values
COMPLETE TRIANGLE3 · 4 · 5
θ ≈ 36.87° · other angle ≈ 53.13°
AREA6
PERIMETER12
sin θ0.6
cos θ0.8
IDENTITY LAB
Check the core identities at one angle
sin²θ + cos²θ1
tanθ = sinθ / cosθ✓
1 + tan²θ = sec²θ✓
1 + cot²θ = csc²θ✓
ALL SIX FUNCTIONS
Exact special-angle forms available.Decimal and exact forms together
UNIT CIRCLE
See x = cos θ and y = sin θ
The point on the circle is (cos θ, sin θ). The ray uses the normalized coterminal angle.
Angle steps
- Convert the input angle to radians.
- Read cosine from x and sine from y on the unit circle.
- Build tangent and reciprocal functions from those two values.
Undefined values are explicittan/sec when cos θ = 0 · cot/csc when sin θ = 0
REFERENCE TABLE
Notable unit-circle angles
Tap an angle to load it into the calculator.
| Angle | Radians | sin | cos | tan |
|---|
DAILY TRIG
One exact-value check per UTC day
Same angle for everyone on the date. Choose the correct trig value before opening a calculator.
TODAY'S QUESTIONsin(30°)
Use quadrant signs and a reference angle, not memorization alone.
Choose an answer.
Formulas, conventions & scope
Six functions
On the unit circle, cos θ is x and sin θ is y. tan θ = sin θ / cos θ. The reciprocal functions are sec = 1/cos, csc = 1/sin and cot = cos/sin.
Inverse trig
arcsin, arccos and arctan return principal values, so the calculator also lists every matching angle in one 0°–360° turn. It does not pretend the principal value is the only solution.
Exact values
Exact radicals are shown for the standard 15° family when recognized. For other angles, the calculator reports a decimal value without inventing a symbolic closed form.
Right triangles
SOHCAHTOA mode is deliberately limited to right triangles. For SSS, SAS, ASA/AAS and SSA ambiguous cases, use the separate Triangle Calculator.