Studied by 3 people
Periodic function
a function where the y values repeat over regular x value intervals
(x,y) → (1/k x
p, ay + q)
min = q
|a|
Calculator
sin⁻¹( ), cos⁻¹( ), tan⁻¹( )
Rearrange
isolate for trig ratios
Factor
exponents, same ratio repeats
Identities
multiple ratios
In all cases
must consider CAST rule
periodic function
a function where the y values repeat over regular x value intervals
period
the duration of one cycle
negative a value
r in x
a value
vertical stretch: |a| > 1; vertical compression: 0 < |a| < 1 --> |a| is the amplitude, |a| = (max - min)/2
k value
horizontal stretch: |k| >1; horizontal compression: 0 < |k| < 1 --> period = 2π/k --> k = 2π/period
p value
horizontal shift --> + left, - right --> moves starting point
q value
vertical shift --> + up, - down --> q = average, q= (max + min)/2
graphing using properties
y-scale:
avg = q
max = q + |a|
min = q - |a|
x-scale:
period = 2π / k
QI (quarter intervals) = Period/4
avg (Sin), max (Cos), avg, min, (and so on)
solving trig equations
1- Rearrange - isolate for trig ratios
2 - Factor - exponents, same ratio repeats
3 - Identities - multiple ratios
In all cases: must consider CAST rule
AROC
slope of secant of curve
IROC
slope of tangent line ( + & - 0.001)
