4.4-4.6 quiz - graphing sinusoid functions, writing equations, and unit circle inverses

parts of an equation

y= a sin/cos (bx+c) + d

a - amplitude

b - period

c - horizontal phase shift

d - vertical shift

Period sin/cos

2π/b

frequency

1/period or b/2π

graphing tan : asymptotes and period

• π/b

• -π/2 & π/2

graphing cot : asymptotes and period

• π/b

• 0 & π

graphing cosecant : asymptotes and period. comp to sin

• 2π/b

• -π & π

  • graph middle asymptote

• sin starts in middle

• down then up

graphing secant : asymptotes and period, comp to cos

• 2π/b

• -π/2 & 3π/2

• cos- starts at first amp

• up then down

unit circle

arcsin

• [-π/2 , π/2]

• Q1, Q4

arccos

• [0,π]

• Q1, Q2

arctan

• [-π/2 , π/2]

• Q1, Q4

Sinusoid word problem

• A = ½(Ymax-Ymin)

• D = ½(Ymax+Ymin)

• B= 2(Xmax-Xmin)

  • Set answer = 2π/b

    • solve for b

• D = -c/b = Xmax

  • solve for c

• Y = a cos (bx + c) + d

Se