Trigonometric Identities, Cheat Sheet of Trigonometry

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Co-function Identities sin@ = cos(*/2-6) sec 8 = csc(x/2-0) tan @ = cot (1/20) = -sin6 csc(-8) = -cscO = cos@ sec(-8) = secO = -tan6 cot (-6) = -coté Addition and Subtraction Identities sin(A+B) = sinAcosB+cos Asin B cos (A+B) = cos Acos B~sin A sinB tan A+tan B tan (A+B) 1—tan A tan B sin(A-B) = sin Acos B—cos A sinB cos(A-B) = cos AcosB+sin A sinB tan(A—B) ~ 2B AtanB (AB) 1+tan A tan B Double-Angle Identities sin26 = 2sin6 cos6 cos26 = cos'@ ~sin"O = 2cos'@ -1 = 1=2sin?e 2tand tan260 = 1=tan’@ Product Identities . 1(.. . sinAcosB = 5 (sina +B) sina B)) cosAsinB = 2 (sinta+B) sin (A B) 2 cosAcosB ; (cos (A +B) +05 (A- B)) sinAsinB) = 2 (cos (a B) cos (A+B) ) 2 https://trigidentities.info TRIGONOMETRIC IDENTITIES Supplement Angle Identities sin(™-8) = sin@ esc(7-8) = cos(x-0) = -cos 6 sec (7-6 ) tan(-0) = -tan@ sin(x+6) ese(™+6) = cos («+ 6) sec(m+8) = tan(m+0) = tand cot(m+6) = Quotient Identities tong - 288 ig - cose _ me cos8 sing tan sec8 = cost esch = sind Pythagorean Identities sin? 6 +cos’6 =1 tan’ @ +1=sec” 6 cot’8 +1=csc@ Half-Angle Identities ne a a 4 [te c0s8 ny 2 8 ©, A [teeose cosy = = V5 ta a _ : 1—cos® nD VV 1+ cose esc @ sec 8 cot(m-8) = -cote =csc 6 -sec 8 cot 8 https://trigidentities.info Sum Identities . . . ( AtB A-B sinA+sinB = 2sinl “> eos “F~ 2 : A+B sinA—sinB = 2cos! A+B cosA +cosB = 2cost “2 A+B A-B cosa cons = 24 A£® unl