List of trigonometric identities

This c an be viewed as a vers ion of the py thagorean

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ))2 and sin2 θ means (sin(θ))2. This c an be viewed as a vers ion of the Py thagorean theorem, and follows from the equationx2 + y2 = 1 for the unit c irc le. This equation c an be s olved for either the s ine or the c os ine: Related identities [edit] Dividing the Py thagorean identity through by either cos2 θ or sin2 θ y ields two other identities : Us ing thes e identities together with the ratio identities , it is pos s ible to ex pres s any trigonometric func tion in terms of any other (up to a plus or minus s ign): Ea ch trigonom e tric function in te rm s of the othe r five .[2] in te rm s of en.wikipedia.or g /wiki/List_of_tr ig onometr ic_identities 1/12 12/7/13 List of tr ig onometr ic identities - Wikipedia, the fr ee encyclopedia Historic shorthands [edit] The vers ine, c overs ine, havers ine, and ex s ec ant were us ed in navigation. For ex ample thehavers ine formula was us ed to c alc ulate the dis tanc e between two points on a s phere. They are rarely us ed today . Na m e (s) Abbre via tion(s) Va lue [3] vers ed s ine, vers ine vers ed c os ine, verc os ine c overs ed s ine, c overs ine c overs ed c os ine, c overc os ine A ll of the tr igonometr ic f unc tions of an angle θ c an be c ons tr uc ted geometr ic ally in ter ms of a unit c ir c le c enter ed at O . Many of thes e ter ms ar e no longer in c ommon us e. half vers ed s ine, havers ine half vers ed c os ine, haverc os ine half c overs ed s ine, hac overs ine c ohavers ine half c overs ed c os ine, hac overc os ine c ohaverc os ine ex terior s ec ant, ex s ec ant ex terior c os ec ant, ex c os ec ant c hord Anc ient Indian mathematic ians us ed Sans k rit terms Jy ā, k oti-jy ā and utk rama-jy ā, bas ed on the res emblanc e of the c hord, arc , and radius to the s hape of a bow and bows tring drawn bac k . Symmetry, shif ts, and periodicity [edit] By ex amining the unit c irc le, the following properties of the trigonometric func tions c an be es tablis hed. Symmetry [edit] W hen the trigonometric func tions are reflec ted from c ertain angles , the res ult is often one of the other trigonometric func tions . This leads to the following identities : Re fle cte d in [4] Shifts and periodicity Re fle cte d in (co-function ide ntitie s)[5] Re fle cte d in [edit] By s hifting the func tion round by c ertain angles , it is often pos s ible to find different trigonometric func tions that ex pres s partic ular res ul...
View Full Document

Ask a homework question - tutors are online