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Arlon Online Engineering Library - TechRef! Trigonometry Trigonometric functions are defined using a right triangle. sin = y/r, cos = x/r tan = y/x, cot = x/y csc = r/y, sec = r/x Law of Sines a/(sin A) = b/(sin B) = c/(sin C) Law of Cosines a2 = b2 + c2 - 2bc cos A b2 = a2 + c2 - 2ac cos B c2 = a2 + b2 - 2ab cos C Identities csc = 1/sin sec = 1/cos tan = sin /cos cot = 1/tan sin2 + cos2 = 1 tan2 + 1 = sec2 cot2 + 1 = csc2 sin ( + ) = sin cos + cos sin cos ( + ) = cos cos - sin sin tan ( + ) = (tan + tan )/(1 - tan tan ) cot ( + ) = (cot cot - 1)/(cot + cot ) sin ( - ) = sin cos - cos sin cos ( - ) = cos cos + sin sin tan ( - ) = (tan - tan )/(1 + tan tan ) cot ( - ) = (cot cot + 1)/(cot - cot ) sin 2 = 2 sin cos cos 2 = cos2 - sin2 = 1 - 2 sin2 = 2 cos2 - 1 tan 2 = (2 tan )/(1 - tan2) cot 2 = (cot2 - 1)/(2 cot ) sin (/2) = ± cos (/2) = ± tan (/2) = ± cot (/2) = ± sin sin = (1/2)[cos ( - ) - cos ( + )] cos cos = (1/2)[cos ( - ) + cos ( + )] sin cos = (1/2)[sin ( + ) + sin ( - )] sin + sin = 2 sin (1/2)( + ) cos (1/2)( - ) sin - sin = 2 cos (1/2)( + ) sin (1/2)( - ) cos + cos = 2 cos (1/2)( + ) cos (1/2)( - ) cos - cos = -2 sin (1/2)( + ) sin (1/2)( - )

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