Precalculus Trigonometric Identities Cheat Sheet, Cheat Sheet of Trigonometry

Download Precalculus Trigonometric Identities Cheat Sheet and more Cheat Sheet Trigonometry in PDF only on Docsity! Pre-Calc Trigonometric Identities The six trigonometric functions/Reciprocals Identities xr y hyp opp x csc 1 sin === xy r opp hyp x sin 1 csc === xr x hyp adj x sec 1 cos === xx r adj hyp x cos 1 sec === x x x y adj opp x cos sin tan === x x xy x opp adj x sin cos tan 1 cot ==== Pythagorean Identities sin2x + cos2x = 1 cos2x = 1 – sin2x sin2x = 1 - cos2x tan2x – sec2x = -1 1 + tan2x = sec2x 1 + cot2x = csc2x Sum or difference of two angles sin(a + b) = sina cosb + cosa sinb cos(a + b) = cosa cosb - sina sinb sin(a - b) = sina cosb - cosa sinb cos(a - b) = cosa cosb + sina sinb ba ba ba tantan1 tantan )tan( − +=+ ba ba ba tantan1 tantan )tan( + −=− Double Angle Formulas Half Angle Formulas cos2x = 1- 2sin2x cos2x = 2cos2x - 1 2 2cos1 sin2 x x −= 2 2cos1 cos2 x x += x x x 2cos1 2cos1 tan2 + −= cos2x = cos2x – sin2x sin2x = 2sinx cosx 2 cos1 2 sin xx −±= 2 cos1 2 cos xx +±= x x x 2tan1 tan2 2tan − = x x x x x xx sin cos1 cos1 sin cos1 cos1 2 tan −= + = + −±= Reduction Formulas Law of cosines a2 = b2 + c2 – 2bc cos A (where A is the angle of a scalene
opposite side a) sin(-x) = -sinx cos(-x) = cosx sin(x) = -sin(x – π) cos(x) = -cos(x – π) Co-Functions tan(-x) = -tanx tan(x) = tan(x – π) sinx = cos(90o – x) cosx = sin(90 o – x)       ±=± 2 cossin π xx       ±=± 2 sincos π xx tanx = cot(90 o – x) secx = csc(90o – x) Sum and Product Formulas sina cosb = ½[sin(a + b) + sin(a - b)] cosa cosb = ½[cos(a + b) + cos(a - b)] cosa sinb = ½[sin(a + b) – sin(a - b)] sina sinb = ½[cos(a – b) – cos(a + b)]       −       +=+ 2 cos 2 sin2sinsin yxyx yx       −       +=− 2 sin 2 cos2sinsin yxyx yx       −       +=+ 2 cos 2 cos2coscos yxyx yx       −       +−=− 2 sin 2 sin2coscos yxyx yx