Return cosine, sine, and tangent from an angle on the unit circle. Each submitted value produces unit-circle point plus the intermediate reasoning.
At angle θ, the unit-circle point is (cos θ, sin θ); tangent is their ratio when cosine is nonzero.
Before accepting Unit-circle point, restore the Unit Circle inputs Angle and Angle unit. Estimate Unit-circle point independently. Then vary Angle unit alone and observe the new Unit Circle output. This isolates the changed part of Unit Circle.
A rounded decimal can hide familiar exact radicals. Tangent is undefined whenever the cosine coordinate is zero.
At 60°, the point is (1/2, √3/2), so tangent is √3.
Convert to a coterminal first-turn angle, locate its quadrant, and use known triangles or coordinate definitions.
Unit Circle uses Angle and Angle unit. Inspect denominators before taking reciprocals or tangent-like ratios. Values near an undefined angle can grow rapidly, so a long decimal is not a sign of stable precision.
For this unit circle result, attach the original angle convention and final rounding place to the answer.
Unit-circle coordinates connect rotations with right triangles, periodic graphs, complex numbers, and oscillation. Unit Circle also relates to vertical coordinate.
Sketch Angle before running Unit Circle. Place Angle unit on the Unit Circle sketch and confirm its unit.
Test a symmetric Unit Circle case. In that Unit Circle case, compare Angle unit with the expected Unit Circle scale.
Before using Unit-circle point downstream, substitute a simple Angle into the same Unit Circle relation. Preserve Angle unit so the comparison remains fair. The resulting Unit-circle point provides a benchmark for detecting a misplaced sign, decimal, or input order.
Preserve the first Unit Circle case before testing another value of Angle. Leave Angle unit unchanged so a shift in Unit-circle point has one cause. Recording both values of Unit-circle point also prevents the revised Unit Circle data from replacing the original silently.
At angle θ, the unit-circle point is (cos θ, sin θ); tangent is their ratio when cosine is nonzero.
Unit-circle coordinates connect rotations with right triangles, periodic graphs, complex numbers, and oscillation.
A rounded decimal can hide familiar exact radicals. Tangent is undefined whenever the cosine coordinate is zero.