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Definition of the Six Trigonometric Functions 2 opp. hyp. sin csc opp. hyp. adj. hyp. cos sec hyp. adj. opp. adj. tan cot adj. opp. Right triangle definitions, where 0 < < Hypotenuse Opposite Adjacent Circular function definitions, where is any angle. y y sin csc r r x2 y2 x cos sec (x,y) r r θ y y x tan cot x x Reciprocal Identities 1 1 sin u cos u csc u sec u 1 1 csc u sec u sin u cos u r y r x x y Negative Angle Identities 1 cot u 1 cot u tan u tan u Tangent and Cotangent Identities sin u cos u tan u cot u cos u sin u Pythagorean Identities sin 2 u cos 2 u 1 1 tan 2 u sec 2 u 1 cot 2 u csc 2 u Cofunction Identities sin u cos u cos u sin u 2 2 csc u sec u sec u csc u 2 2 tan u cot u cot u tan u 2 2 sin( u ) sin u csc( u ) csc u cos(u ) cos u sec( u ) sec u cot( u ) cot u tan( u ) tan u Sum and Difference Formulas sin( u v) sin u cos v cos u sin v cos(u v) cos u cos v sin u sin v tan u tan v tan( u v) 1 tan u tan v Half Angle Identities 1 cos u u sin 2 2 1 cos u u cos 2 2 1 cos u u tan 1 cos u 2