General Graphs of Sine and Cosine

Radian: 1 radian is the length of 1 radius bend around the arch.
1 radian ≈ 57.29°

Sinusoids y=a sin b(x-c)+d, y=a cos b(x-c)+d

d- vertical translation
c- horizontal translation (phase shift)
a- amplitude (vertical stretch) if negative it reflects over X axy
b- horizontal strectch/shrink (frequency)

** ∏=pie (3.14)


Sine
» Domain: (-∞,∞)
» Range: [1,-1]
» Period: 2∏
» Zeros: ∏n n=any integer


Cosine
» Domain: (-∞,∞)
» Range: [1,-1]
» Period: 2∏
» Zeros: ∏/2 + ∏n n=any integer



ex: y=3cos 2(x-∏/4)+ 1

period: 2∏/2 = ∏
incrament: ∏ /4
a: 3
horizontal shift: ∏ /4
vertical shift: 1