Trigonometry Identities
Basic and Pythagorean Identities \csc(x) = \dfrac{1}{\sin(x)} csc ( x ) = sin ( x ) 1 \sin(x) = \dfrac{1}{\csc(x)} sin ( x ) = csc ( x ) 1 \sec(x) = \dfrac{1}{\cos(x)} sec ( x ) = cos ( x ) 1 \cos(x) = \dfrac{1}{\sec(x)} cos ( x ) = sec ( x ) 1 \cot(x) = \dfrac{1}{\tan(x)} = \dfrac{\cos(x)}{\sin(x)} cot ( x ) = tan ( x ) 1 = sin ( x ) cos ( x ) \tan(x) = \dfrac{1}{\cot(x)} = \dfrac{\sin(x)}{\cos(x)} tan ( x ) = cot ( x ) 1 = cos ( x ) sin ( x ) 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. The following (particularly the first of the three below) are called "Pythagorean" identities. sin 2 ( t ) + cos 2 ( t ) = 1 tan 2 ( t ) + 1 = sec 2 ( t ) 1 + cot 2 ( t ) = csc 2 ( t ) Note that the three identities above all involve squaring and ...