Cofunction Calculator

Cofunctions are one of the neat symmetries hiding inside trigonometry, and this calculator lays them out clearly for any angle you choose. The idea is that the six trig functions come in three matching pairs, sine with cosine, tangent with cotangent, and secant with cosecant, and the value of one function at an angle is always equal to the value of its partner at the complementary angle, the angle that brings the total up to 90 degrees. That is exactly why the names of three of them start with co, as in cosine, cotangent and cosecant: the co is short for complementary. Enter an angle in degrees and the calculator shows its complement, then sets out each cofunction identity with the actual values, so you can see at a glance that the sine of your angle really does equal the cosine of the complement, and so on for the other pairs. The reasoning behind it is beautifully simple and worth knowing: in a right-angled triangle the two non-right angles always add to 90 degrees, and the side that is opposite one of them is the side that is adjacent to the other, so swapping the roles of opposite and adjacent turns sine into cosine and back again. These identities are a standard part of NCEA and senior trigonometry, useful for simplifying expressions, proving other identities, solving equations and rewriting a function in terms of its cofunction, which can make a problem much easier. Because the calculator updates as you type, you can explore how the pairs stay locked together as the angle changes, and confirm special cases like the sine and cosine of 45 degrees being equal because 45 is its own complement. The identities and a worked example are explained clearly below.

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