TRIGONOMETRY FORMULAS Angle Addition Formulas Difference Formulas sin(α + β ) = sinα cos β + cosαsin β sin(α − β ) = sinα cos β − cosαsin β cos(α + β ) = cosα cos β − sinα sin β cos(α − β ) = cosαcos β + sinα sin β tan (α + β ) = tan a + tan β 1 − tan α tan β tan (α − β ) = tan a − tan β 1 + tan α tan β Half Angle Formulas Double Angle Formulas sin(2θ) = 2 sin θ cosθ cos(2θ) = cos θ − sin θ 2 2 = 1 − 2 sin 2 θ = 2 cos2 θ − 1 tan (2θ) = 2 tanθ 1 − tan 2 θ u 1− cosu sin = ± 2 2 u 1+ cosu cos = ± 2 2 u 1− cosu tan = ± 2 1+ cosu 1 − cosu = sinu sinu = 1 + cosu Product-to-Sum Formulas u + v u − v sin u + sin v = 2sin cos 2 2 1 [cos( A − B ) − cos( A + B )] 2 1 cos A cosB = [cos( A − B ) + cos( A + B)] 2 1 sin A cos B = [sin( A + B ) + sin ( A − B )] 2 1 cos Asin B = [sin( A + B ) − sin ( A − B )] 2 sin A sin B sin C = = a b c Law of Cosines SAS Form c 2 = a 2 + b 2 − 2ab cosC b 2 = c 2 + a 2 − 2ca cos B a 2 = b 2 + c 2 − 2bc cos A 1 − cos(2θ ) 2 1+ cos(2θ ) cos 2 θ = 2 1 − cos(2θ) 2 tan θ = 1 + cos(2θ) sin 2 θ = Sum-to-Product Formulas sin Asin B = Law of Sines Power Reducing Formulas u + v u − v sin u − sin v = 2 cos sin 2 2 u + v u − v cosu + cosv = 2 cos cos 2 2 u + v u − v cosu − cosv = −2 sin sin 2 2 Law of Cosines SSS Form Area of a Triangle (SAS) b +c − a 2 bc c2 + a 2 − b2 cos B = 2ca a 2 + b 2 − c2 cosC = 2ab cos A = 2 2 2 = absin C bcsin A casin B = = 2 2 2 Heron’s Formula (SSS) s= a+b +c 2 Area = s (s − a)(s − b )( s − c )