The unit circle turns an angle into exact horizontal and vertical coordinates, which are cosine and sine.
Use it to read an angle’s sine and cosine from one consistent radius-one model.
The relationship
Write the rule before calculating
Use the reference angle and quadrant signs with unit-circle exact values.
See the structure
What the calculation is doing
cos θ•sin θUse the reference angle and quadrant signs with unit-circle exact values.
Worked interpretation
Read the result in context
At 75°, tan θ = 2 + √3.
Interpret with care
Important boundary
Exact values depend on the stated angle unit and quadrant; signs change around the circle.
Use the Mathematics collection to move between connected concepts without duplicating the calculation.
Quick guide
How to use this calculator
Enter the known values and choose degrees or radians where the page offers a unit selector.
Select the intended function, identity family, or solve direction when needed.
Read the primary answer first, then inspect domain notes, supporting values, or the graph.
Calculation method
Apply the selected trigonometric relationship
Use the reference angle and quadrant signs with unit-circle exact values.
The calculator validates real-function domains and reports undefined angles or impossible triangles explicitly instead of displaying NaN, Infinity, or a misleading zero.
Worked example
Worked example
At 75°, tan θ = 2 + √3.
Use the reference angle and quadrant signs with unit-circle exact values.
Supported inputs
Precision and limits
Angle units
Degree/radian selectors apply only to fields labelled as angles. Triangle-law angles are explicitly entered and returned in degrees. Sinusoidal model arguments are explicitly radians.
Numerical precision
Calculations use finite double-precision arithmetic and normally display 12 significant digits. Exact-value pages return symbolic radical forms only for their stated standard-angle table.
Supported magnitude
Numeric inputs may be zero or have absolute magnitude from 1e-100 through 1e100. This bounded range prevents floating-point underflow and overflow from being shown as meaningful results.
Domains and branches
Reciprocal functions reject their true zero denominators. Inverse functions use the principal real branch stated by the calculator, while periodic equation solving lists every solution in the selected closed interval.
Calculator-specific rule
Exact radical lookup is supported for multiples of 15° (π/12). Other angles belong in the numerical Trigonometry Calculator.
