Sine and Cosine Addition FormulasVideos, worksheets, games and acivities to help PreCalculus students learn about the sine and cosine addition formulas.
Cosine Addition Formula : The cosine addition formula calculates the cosine of an angle that is either the sum or difference of two other angles. It arises from the law of cosines and the distance formula. By using the cosine addition formula, the cosine of both the sum and difference of two angles can be found with the two angles' sines and cosines.
Sine Addition Formula : Starting with the cofunction identities, the sine addition formula is derived by applying the cosine difference formula. There are two main differences from the cosine formula: (1) the sine addition formula adds both terms, where the cosine addition formula subtracts and the subtraction formula adds; and (2) the sine formulas have sin-sin and cos-cos. Both formulas find values for angles.
Using the Sine and Cosine Addition Formulas to Prove Identities : Applying the cosine addition and sine addition formulas proves the cofunction, add pi, and supplementary angle identities. Using the formulas, we see that sin(pi/2-x) = cos(x), cos(pi/2-x) = sin(x); that sin(x + pi) = -sin(x), cos(x + pi) = -cos(x); and that sin(pi-x) = sin(x), cos(?-x) = -cos(x). The formulas also give the tangent of a difference formula, for tan(alpha-beta).
Custom Search
We welcome your feedback, comments and questions about this site - please submit your feedback via our Feedback page. © Copyright 2005, 2011 - onlinemathlearning.com Embedded content, if any, are copyrights of their respective owners.
|
Custom Search