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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  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 .
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  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  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
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  By ex amining the unit c irc le, the following properties of the trigonometric func tions c an be es tablis hed. Symmetry  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  Shifts and periodicity Re fle cte d in
(co-function ide ntitie s) Re fle cte d in  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...
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