ELEMENTS OF PLANE TRIG ONOMETRY A SERIES OF MATHEMATICAL TEXTS ED I T ED BY EARLE RAYMOND HEDRICK THE CALCULU S By ELLER Y WILLIA MS DAVI S and WILLIAM CHA R LE S B RE N K E . ANALYTIC GEOMETRY AND ALGEBRA B E X N D E R Z IW E T LO U I S E N O K S y A L A and A LL H P IN . ELEMENTS O F A NALYTIC GEOMETRY B A X D ZI WE T L I A O K S y LE AN ER and OU S LLEN H P IN . PLANE AND SPHERICAL TR IGONOMETRY WITH COM PLETE TABLE S B A LF RE D MO N RO K Y O I N GO y E EN N and LO U S I L D . P LANE AND SP HERICAL TR IGO NOMETRY WITH B RIEF T ABLE S B L F R E D y A D MONROE KE N YON and LO U I S IN G O L . ELE MENTARY MAT HEMATICAL A NALYSIS B J O HN E LE Y YO U N G K MI E T T MORGAN y W S and FRAN LL . COLLEG E ALGE BRA B R E S T BR W y E N O N S KINNER . ELEMENTS OF P LANE TR I GONOM ETRY WITH COM F LET E TABLES B A LF R M E K YO LO U I IN GO L y ED ONRO EN N and S D . ELEMENTS O F P L ANE TR I GONO METRY WITH BRIEF TABLE S B A F D E KE N Y N U IS IN GO L y L RE MON R O O and LO D . THE MACMILLAN TA BLES P re re h f E AR E R Y O D D pa d under t e directi on o L A M N HE RI CK . PLANE GE O METRY W O H S By ALTER B U RT ON F R D and C ARLE AMMERMAN . PLAN E AND SOLI D GEO METRY B W B OR H R E S A y ALTER URTON F D and C A L MMERMAN . SOLID G EOMETRY B W T E B U N F OR H S M M E R M N y AL R R TO D and C ARLE A A . CONSTR UCTIVE GEO METRY P u r h f E AYM D H RI K repared nd e t e direction o EARL R ON ED C . JUN IO R HIG H SC HO O L MATHEM ATICS B W L B . EN T E M N . F W. y . VOS URGH and G L A Th is b o o k is issued in a fo rm identical With that o f the b oo ks anno unced abo ve ELEMENTS OF PLANE TRIGONOMETRY BY ALF RED MO NRO E KENYO N F E O F M AT H M AT I CS P U R U U VE S TY PRO SSOR E , D E NI R I A N D LO UI S ING O LD ASSISTANT PRO F ESSOR O F MATHEMATICS T HE U NI VE RSITY O F M I S S O URI N amEa th THE MACMILLAN CO MPANY 1 91 9 All ria hta reserved PY I T 19 CO R G H , 19 , BY THE M ACM ILLAN CO MPAN Y . e e Published A ril 1 1 . Set u p a nd lectro ty p d. p , 9 9 Nurim ob 19m m in o Berwick Smith Co . a sh C . J . S . C g A . N orwood, Ma ss . , U .S . PREFACE THI S book ca rrie s o u t the chief motive s which guided the a uthors in their la rger work on Pla n e a n d Spherica l Trigon o m r On a ha s n r r r a n d et y . the other h nd it been e ti ely ew itten , a r in a ra r ha s been ma de s till more element y ch cte . The new text form s a trea tment of P la ne T rigono metry which is q uite bu t r ss a s s s s a brief, which neve thele de l with the mo t e enti l topics in more tha n the u sua l deta il . Thi s ha s been a cco mpli shed by o mitting o r cu rt a iling certa in topics tha t a re seldo m u s ed by the s tudent except in some rk s a ll r a r s pecia l lin e of wo . Thu of Sphe ic l T igon om etry a n d m u ch of the deta iled dis cu ssion of T rigono metric Identities u n s is o ra na a n d Eq a tio mitted . Such t ditio l topics a s De ’ M oivre s Theorem a n d in fin ite s e ries were omitted from the ’ a uthor s la rger work beca u se they ha ve few a pplica tion s with ’ s a re in the s tudent s pre sent g ra sp . The e of cou rs e omitted r s k a s fro m the p e ent boo l o . Thu s thi s trea tment conta in s a minim u m of pu rely th eo reti Its r za n is ca l ma tter . enti e orga ni tio intended to give a clea r v a s s s r iew of the im medi te u efulne of trigonomet y. s o r a s r a s r a The lution of T i ngle e m in the p incip l motive . As s s r is a a k a a n d is s uch, thi p oble m tt c ed im medi tely it pu hed fi i to a de n te conclu s ion ea rly in the cou rse . More complete outlin e s tha n u sua l ha ve been given fo r the s u r r n h s ol tion of obliqu e tria ngle s by m ea n s of ight t ia gles . T i method of solution wa s empha siz ed recently in the Sylla bu s of W r D r a r f r i r in S . A. T A the epa tment o n st uction the . C. ve y brief cou rse cou ld well clo se with thi s m ethod of s olving tri a n s gle . Other p ra ctica l p roblem s a re introduced to furn ish a motive fo r r a n ra a a r s the t e tm ent of the ge e l ngle , the ddition theo em , ra m . m s a ea sure etc. Am n r a a s di n , o g othe pplic tion , the co po i V PREFACE n a nd r s n s r s a n d a u a r s tio e olutio of force , p oj ection , ng l peed a re introduced pro min ently . r n d s A is The ta ble s a e very complete a u a ble . ttention a a r a r a s a r s s a r s u s c lled p ticul ly to the t ble of q u e , q u e root , c be , b its u se P a r a r a n d s n la w etc. y the yth go e n theo e m the co i e u se become p ra ctica ble for a ctu a l computa tion . The of the slide rule a n d o f four-pla oe ta bles is enco ura ged fo r p roblem s r r On e k tha t do n o t dema nd ext eme a ccu a cy. edition of the boo n a s - a a es M a who u se a co t in only the four pl ce t bl . ny th t edi tion fin d it a dvi sa ble to ha v e s tudents purcha s e a l s o the five pla ce ta ble s which a re publi shed s epa ra tely bo und under the M a a a s title The cmill n T ble . The a uthors ha ve bo rn e in m ind con s ta ntly the n eeds of the beginner in trigonometry a n d ha ve a da pted the book to u se in s o a s ra a ec nd ry s chool s a s well a s in colleges . Illu t tiv e m te r a a o n s a n d a a s a e a r i l b u d , the expl n tion h ve b en c efully rk in s f s u wo ed out g rea t deta il . The a mple form s o r the ol r a n s is a s r k n s a s n tion of t i gle t i i g in t nce of thi te dency.