Trig Review

In mathematics, an "identity" is an equation which is always true. These can be "trivially" true, like "x = x" or usefully true, such as the Pythagorean Theorem's "a2 + b2 = c2" for right triangles. There are loads of trigonometric identities, but the following are the ones you're most likely to see and use.

Notice how a "co-(something)" trig ratio is always the reciprocal of some "non-co" ratio. You can use this fact to help you keep straight that cosecant goes with sine and secant goes with cosine. sin2(t) + cos2(t) = 1 tan2(t) + 1 = sec2(t) 1 + cot2(t) = csc2(t) The above, because they involve squaring and the number 1, are the "Pythagorean" identities. You can see this clearly if you consider the unit circle, where sin(t) = y, cos(t) = x, and the hypotenuse is 1. sin(–t) = –sin(t) cos(–t) = cos(t) tan(–t) = –tan(t) Notice in particular that sine and tangent are odd functions, while cosine is an even function.