The Ungerecht Family Tree

transformations of sine or cosine function: y = a * sin(k(x + c)) + d

a = amplitude, -c = phase shift, d = vertical shift, 2pi/k = period for tan, the period is pi/k

double angle: 2theta

sin(2theta) = 2sin(theta)cos(theta)
cos(2theta) = cos^2(theta) - sin^2(theta)
            = 2*cos^2(theta) - 1
            = 1 - 2*sin^2(theta)

negative angles:

sin(-theta) = -sin(theta)
cos(-theta) = cos(theta)  => tan(-theta) = -tan(theta)

additive, subtractive: sin(a+b) = sin(a)cos(b) + cos(a)sin(b) cos(a+b) = cos(a)cos(b) - sin(a)sin(b) sin(a-b) = sin(a)cos(b) - cos(a)sin(b) cos(a-b) = cos(a)cos(b) + sin(a)sin(b)

complements: sin(theta) = cos(pi/2 - theta) cos(theta) = sin(pi/2 - theta)