Trig Cheat Sheet: Definition of the Trig Functions

Trig Cheat Sheet Definition of the Trig Functions Right triangle definition For this definition we assume that Unit circle definition 0

Formulas and Identities Tangent and Cotangent Identities Half Angle Formulas cos0 tan cot sin' 9 = - (1-cos (29) Reciprocal Identities sin O 1 csc0 1 1 sec cos 0 sec0 Sum and Difference Formulas tan O = 1 sin (a+B) = sin a COS B I cos acis tan G cote Pythagorean Identities COS (a+B) = COS + sin a sin tan 0 +1 = sec20 tan a(asp) tan +cot20 = csc2 O Product to Sum Formulas Even/Odd Formulas sin a sin (-0) = - sin O esc(-0)== = - csc0 COS a COS COS (-0) = cos e (-0) = sec A tan (-0) = - tan ot(-)) - cot O sin a COS Periodic Formulas If n is an integer. COS a sin ++2nn) = sin G :(0+2nn)= = csc@ Sum to Product Formulas COS (O+2nn) = cos Q sec(0+2n) = sec 0 = tan (0+n) = tan 0 cot (0+xn) = cot6 Double Angle Formulas COS sin(20)=2sine cost = cos a+cos = 2 cos 2 - 1 -2sin2 cos a - COS = sin(a+P)sin(a-p sin tan (28)=2100 2 O Cofunction Formulas Degrees to Radians Formulas - cos (-0)=sint If x is an angle in degrees and t is an angle in radians then - csc0 180 x T = t = and 180 TOX and 180t = cot A -tan = tan 0

Unit Circle y (0,1) 70 1 V3 ( 1 3 2' 2 2 2 2 . TT 2n 2 2 2 2 90° ( 3 2 2 2 2 3 120° 60° TT 3 4 V3 1 2 1 4 2 2 135° 45° T 5T 6 6 30° 150° (-1,0) T 180° 0° 0 (1.0) 360° 2 x 210° 7 330° 11 6 225° ( 5 1 6 315° 3 1 5 2 2 240° 4 300° 7 n ( 2 V2 4 270° 5T 4 V2 2 V2 2 3 3 3 2 2 2 1/5 1 V3 2' 2 (0,-1) For any ordered pair on the unit circle (x,y) : cos e = x and sin O =y Example COS -12 5 3 2 sin ( 5 3 V3 2

Inverse Trig Functions Definition Inverse Properties y=sin is equivalent to X= sin y cos(cos-'(x))=x y= =cos is equivalent tox= cosy n(sin-1(x))=x sin-1(sin(0))=0 y = tan1 is equivalent tox= tan y n(tan-1(x))=x Domain and Range Function Domain Range Alternate Notation sin" x = arcsin x -1