Saturday, October 10, 2020

Sines and Cosines: Adding and Subtracting Angles

 Sines and Cosines:   Adding and Subtracting Angles





Note:   


π/2 radians = 90°,   π radians = 180°


Sine


sin(x + π/2) = sin(x) cos(π/2) + cos(x) sin(π/2) = cos(x)


sin(x - π/2) = sin(x) cos(π/2) - cos(x) sin(π/2) = -cos(x)


sin(π/2 - x)  = sin(π/2) cos(x) - cos(π/2) sin(x) = cos(x)


sin(x + π) = sin(x) cos(π) + cos(x) sin(π) = -sin(x)


sin(x - π) = sin(x) cos(π) - cos(x) sin(π) = -sin(x)


sin(π - x)  = sin(π) cos(x) - cos(π) sin(x) = sin(x)


Cosine


cos(x + π/2) = cos(x) cos(π/2) - sin(x) sin(π/2) = -sin(x)


cos(x - π/2) = cos(x) cos(π/2) + sin(x) sin(π/2) = sin(x)


cos(π/2 - x) = cos(π/2) cos(x) + sin(π/2) sin(x) = sin(x)


cos(x + π) = cos(x) cos(π) - sin(x) sin(π) = -cos(x)


cos(x - π) = cos(x) cos(π) + sin(x) sin(π) = -cos(x)


cos(π - x) = cos(π) cos(x) + sin(π) sin(x) = -cos(x)


Eddie


All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


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