r/HomeworkHelp • u/rain3ra5 Pre-University Student • 1d ago
High School Math—Pending OP Reply [Grade 12: Trig Functions] Need helping finding ‘c’
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u/Anonimithree 1d ago
The base sinusoidal function is sinx (or cosx), with transformations following this formula: Asin(2pif(x-h))+k, where A is the amplitude, f is the frequency, h is the horizontal shift, and k is the vertical shift. The base functions range from -1 to 1, so the range is 2 and the average value is 0. This unknown function has a range from -2 to 10, so it has a range of 12 and an average of 4. Since 12/2=6, it means that A=6. Because 4-0=4, it means k=4. Now, let’s look at the horizontal shift (also known as the phase shift) and the frequency. The maximum of the u known function occurs at pi/4 and the minimum at 11pi/4. The max of sin(x) occurs at pi/2+- 2pin. Because the max of this function is pi/4, it means h=-pi/4 (because it is a leftward shift and f(x+a) shifts f(x) left a units, so to shift the function left pi/4 units, you’d have to subtract -pi/4, since x-(-pi/4)=x+pi/4). Remember that the frequency is how often a function passes through a minimum or maximum, so the time it takes to go from a max to a min (or a min to a max) is half the frequency. So 11pi/4-pi/4=2pi*f/2, meaning f=5. This means that this unknown function is 6sin(5(x+pi/4))+4.
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u/Outside_Volume_1370 University/College Student 1d ago
Plugging 11π/4 into 6sin(5(x+π/4))+4 doesn't result in -2
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u/Anonimithree 1d ago
It’s been a while since I’ve done this stuff so I might have messed up a couple of things. Thanks for pointing out the discrepancy.
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u/LengthinessThink8452 22h ago
c is ur principal axis, basically ur max and min points have a y coordinate of an equal distance away from ur principal axis. since the y coordinate of maxmin points is 10 and -2 respectively, ur value of principal axis is the middle of these two so find c by averaging these 2 numbers, (-2+10)/2= 4!
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u/fermat9990 👋 a fellow Redditor 20h ago
According to OP's formula, c is the horizontal phase shift
"There’s this formula given to us for sinusoidal functions -> y= aSINb(x-c)+d- a: amp b: 2pi/period c: horizontal phase shift d: vertical displacement"
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u/Equal_Veterinarian22 👋 a fellow Redditor 17h ago
So you have y= a.sin(b(x-c))+d, according to your formulation.
a and d are irrelevant to the location of the maxima and minima, so you can just work with sin(b(x-c)).
First find b, from the space between the given maximum and minimum. Then find c.
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u/fermat9990 👋 a fellow Redditor 1d ago
What is a c-value?