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Unformatted text preview: eads [c i tati on needed] en.wikipedia.or g /wiki/List_of_tr ig onometr ic_identities 7/12 12/7/13 List of tr ig onometr ic identities  Wikipedia, the fr ee encyclopedia where and See als o Phas or addition. Lagrange's trigonometric identities [edit] Thes e identities , named after Jos eph Louis Lagrange, are:[28][29] A related func tion is the following func tion of x, c alled the Diric hlet k ernel. Other sums of trigonometric f unctions [edit] Sum of s ines and c os ines with arguments in arithmetic progres s ion:[30] if , then For any a and b : where atan2(y, x) is the generaliz ation of arc tan(y/x) that c overs the entire c irc ular range. The above identity is s ometimes c onvenient to k now when think ing about the Gudermannian func tion, whic h relates the c irc ular and hy perbolic trigonometric func tions without res orting
toc omplex numbers .
If x, y, and z are the three angles of any triangle, i.e. if x + y + z = π, then Certain linear f ractional transf ormations [edit] If ƒ(x) is given by the linear frac tional trans formation and s imilarly then More ters ely s tated, if for all α we let ƒα be what we c alled ƒ above, then If x is the s lope of a line, then ƒ(x) is the s lope of its rotation through an angle of − α. I nverse trigonometric f unctions [edit] en.wikipedia.or g /wiki/List_of_tr ig onometr ic_identities 8/12 12/7/13 List of tr ig onometr ic identities  Wikipedia, the fr ee encyclopedia Compositions of trig and inverse trig functions Relation to the complex exponential f unction [edit] [edit] [31] (Euler's formula), (Euler's identity ),
[32] [33] and henc e the c orollary : where . I nf inite product f ormulae [edit] For applic ations to s pec ial func tions , the following infinite produc t formulae for trigonometric func tions are us eful:[34][35] I dentities without variables [edit] The c urious identity is a s pec ial c as e of an identity that c ontains one variable: Similarly : The s ame c os ine identity in radians is Similarly : The following is perhaps not as readily generaliz ed to an identity c ontaining variables (but s ee ex planation below): Degree meas ure c eas es to be more felic itous than radian meas ure when we c ons ider this identity with 21 in the denominators : en.wikip...
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