How this calculator works
In a right triangle, the side opposite one acute angle is adjacent to the other. This exchanges sine with cosine and tangent with cotangent; taking reciprocals exchanges secant with cosecant. The identities also hold beyond acute angles wherever both expressions are defined. At singular angles both matching expressions are displayed as Undefined.
Formula
sin θ=cos(π/2-θ); tan θ=cot(π/2-θ); sec θ=csc(π/2-θ), with the reverse identities obtained by swapping each pair.
Worked example
sin 30° = cos 60° = 0.5. cot 45° = tan 45° = 1. sec 0° = csc 90° = 1.
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Frequently asked questions
Must the two angles add to 90°?
Yes. That is the meaning of complementary. Supplementary angles add to 180° and use different identities.
Can I use radians?
Yes. A right angle is π/2 radians or one-quarter of a turn. The unit selector converts before calculation.
What happens at an undefined angle?
For example tan 90° and cot 0° both divide by zero. Both readouts show Undefined.