sin (a+-b)
sin a cos a +- cos b sin b
cos (a+b)
cos(a-b)
think opposite sign, cos cos sin sin
ex. for cos (a+b)
cos a cos b - sin a sin b
how to find θ
θ=s/r
s = arc length
BOBO - bigger on bottom 0
HA at y=0
BETC - same degree
Ratio of leading coefficients = HA (y=ratio)
BOTU - bigger on top
slant asymptote
leading coefficients + x’s on bottom and top, reduce x’s
Vertical asymptotes in rational functions
factor left in the denominator = VA
if a hole occurs as well, the hole just occurs inside the VA.
VA takes precedence
residual = actual - predicted (model)
pattern = NOT appropriate
Neg residual = overestimate
Pos residual = underestimate
exponential growth
growing away from 0
exponential decay
coming to 0
exponentials
always inc or dec
end behavior → neg inf, pos inf, or 0, ONE SIDE will be 0