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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