REFERENCE page 2 TRIGONOMETRY Angle Measurement Fundamental Identitie T radians-18 1 rad ,1809 s=0 m0-8 (0in radians) cot tan 0 sin+cos Right Angle Trigonometry 1+tan'0-scc0 1+cot0=csc0 csc o-hyp opp sin(-0)=-sin cos(-8)=cos8 tan(-0)=-tan 8 m号-0）-m0 m0- co5-0）=sng tan(-)-co.o Trigonometric Functions The Law of Sines in csc sinA sin B sin C sec an 6= The Law of Cosines +e2-2bc cosA b2=a+e2-2ac cos B a+b-2ab cos C Addition and Subtraction Formulas sin(x +y)=sin x cos y cosx sin y in(r-y)=sinx cosy -cosx siny cosx+y)=cosx cosy sinx sin y 国 cos(x-y)=cos x cos y sinx sin y an(r+y)= tanx tan y 1 tanx tan y Double-Angle Formulas Trigonometric Functions of Important Angles sin 2x =2 sin x cosx cos 2x =cos-sinx=2 cos-1=1-2sin radians sin 6 cos 8 tan 6 tan 2x 1-tan'x 2 tan x 0 6 /2 5/2 v3/3 45 /4 √2/2 2/2 Half-Angle Formulas 60 5/2 1/2 90° π/2 0 -cos 2x cos+cos 2x 2TRIGONOMETRY REFERENCE page 2 Fundamental Identities csc  − 1 sin  sec  − 1 cos  tan  − sin  cos  cot  − cos  sin  cot  − 1 tan  sin2  1 cos2  − 1 1 1 tan2  − sec2  1 1 cot2  − csc2  sins2d − 2sin  coss2d − cos  tans2d − 2tan  sinS  2 2 D − cos  cosS  2 2 D − sin  tanS  2 2 D − cot  The Law of Sines sin A a − sin B b − sin C c A b c a B C The Law of Cosines a 2 − b 2 1 c 2 2 2bc cos A b 2 − a 2 1 c 2 2 2ac cos B c 2 − a 2 1 b 2 2 2ab cos C Addition and Subtraction Formulas sinsx 1 yd − sin x cos y 1 cos x sin y sinsx 2 yd − sin x cos y 2 cos x sin y cossx 1 yd − cos x cos y 2 sin x sin y cossx 2 yd − cos x cos y 1 sin x sin y tansx 1 yd − tan x 1 tan y 1 2 tan x tan y tansx 2 yd − tan x 2 tan y 1 1 tan x tan y Double-Angle Formulas sin 2x − 2 sin x cos x cos 2x − cos2 x 2 sin2 x − 2 cos2 x 2 1 − 1 2 2 sin2 x tan 2x − 2 tan x 1 2 tan2 x Half-Angle Formulas sin2 x − 1 2 cos 2x 2 cos2 x − 1 1 cos 2x 2 Angle Measurement  radians − 1808 r r ¨ s 18 −  180 rad 1 rad − 180°  s − r s in radiansd Right Angle Trigonometry sin  − opp hyp csc  − hyp opp ¨ opp adj hyp cos  − adj hyp sec  − hyp adj tan  − opp adj cot  − adj opp Trigonometric Functions sin  − y r csc  − r y (x, y) r ¨ x y cos  − x r sec  − r x tan  − y x cot  − x y Graphs of Trigonometric Functions π 2π x y y=cot x x 1 _1 y π 2π y=csc x y=sec x π 2π x y 1 _1 x y π 2π y=tan x y=cos x π 2π x y 1 _1 y=sin x x y 1 _1 π 2π Trigonometric Functions of Important Angles  radians sin  cos  tan  08 0 0 1 0 308 y6 1y2 s3y2 s3y3 458 y4 s2y2 s2y2 1 608 y3 s3y2 1y2 s3 908 y2 1 0 — Copyright 2021 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it