The Ungerecht Family Tree

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

(Graphics from www.Desmos.com, labeling was added) a = amplitude, c = phase shift, d = vertical shift, 2π/b = period (for tan the period is π/b)

double angle: 2θ

sin(2θ) = 2sin(θ)cos(θ)
cos(2θ) = cos²(θ) - sin²(θ)
        = 2*cos²(θ) - 1
        = 1 - 2*sin²(θ)

negative angles:

sin(-θ) = -sin(θ)
cos(-θ) = cos(θ)
tan(-θ) = -tan(θ)

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

• https://www2.clarku.edu/faculty/djoyce/trig/identities.html
• 11 pages of definitions, postulates and theorems: http://www.ouchihs.org/ourpages/auto/2013/7/26/52822673/Geo-PostulatesTheorems-List.pdf

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