12-05: Trigonometric Equations

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MHF4U

Ontario

12th

Last updated 7:55 PM on 8/21/22
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19 Terms

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