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


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