Geometry: An Interactive Journey to Mastery



Formulas

Trigonometry: Through Right Triangles

sin x opphyp.

cos x (^) hypadj.
tan x oppadj sincos^ xx.
Addition Formulas
sin xy sin xcos ycos xsin y.
cos xy cos xcos ysinxsin y.
Changing yWRíyWKHVHUHDGͼ௘XVLQJsin  yy yysin and cos cos ௘ͽDVIROORZV
sin xy sin xcos ycos xsin y.
cos xy cos xcos ysinxsin y.
3XWWLQJy = xLQWRWKH¿UVWHTXDWLRQVJLYHVWKHIROORZLQJ
sin 2 xxx 2 sin cos.
cos 2 xx x  cos^22 sin.
ͼ௘7KLV¿QDOHTXDWLRQLVRIWHQDEEUHYLDWHGDVcos 2 xxx cos^22 sin .௘ͽ
law of cosines: If a triangle has sides a, b, and c with angle xEHWZHHQVLGHVa and b, then
cab ab x^222 ^2 cos^.^
Scale
,QVFDOLQJE\DIDFWRUk,
x DOOOHQJWKVFKDQJHE\DIDFWRUk.
x DOODUHDVFKDQJHE\DIDFWRUk^2.