#Trig equation

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white adder
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Determine a sinusoidal equation if it has a max of 16, min of 4, period of 12 and passes through the point (3,4)

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white adder
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So I know that the amplitude is 6

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and the axis of curve is y=10

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and the k value is 30

summer wedge
white adder
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but im not sure how to solve for phase shift

summer wedge
white adder
white adder
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16+4/2 = 10

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so y=10

summer wedge
white adder
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its alr

summer wedge
# white adder

Oh. A bit of an odd form. I'm more used to f(x) = A cos(ωx + φ0) + B.

white adder
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interesting

summer wedge
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In any case, your k is my ω.

white adder
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is that the standard form in textbooks?

summer wedge
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In which case ω should be 2π/12 = π/6, rather.

summer wedge
white adder
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I see

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im also not sure if i should use sine or cosine

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would it make a difference

summer wedge
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Doesn't matter.

white adder
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ok

summer wedge
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The only thing that will differ is the initial phase.

white adder
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so so far i have f(x)=6sin(30(x-c))+10

summer wedge
white adder
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because k=360/12

summer wedge
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The relation connecting the period and frequency is ω = 2π/T.

summer wedge
white adder
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yes 30 degrees

summer wedge
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If so, yeah, k = 30°.

white adder
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my bad

summer wedge
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So, we have:
f(x) = 10 + 6sin(30°(x - d))
We know that f(3) = 4. So, try using that to find d.

white adder
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hmm okay so i sub in the point?

summer wedge
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Yeah.

white adder
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ok ill try and show u

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but my algebra is bad

summer wedge
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Well, you do need to remember how to solve elementary trigonometric equations.

white adder
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Idk how to isolate💔

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Oops

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I wrote +10 again

summer wedge
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Bring the equation to the elementary form first.

white adder
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Elementary?

white adder
summer wedge
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Elementary trigonometric equations have a form f(x) = a, where the f(x) is a trigonometric function.

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So, isolate the trigonometric function first.

white adder
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So divide 6sin?

summer wedge
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Well, bring all the constant terms to the right first. Then yes.

white adder
summer wedge
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Uh...

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That makes no sense.

white adder
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Yeah idk what I’m doing 💔💔

summer wedge
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We have:
10 + 6sin(30°(3 - d)) = 4
6sin(30°(3 - d)) = -6
sin(30°(3 - d)) = -1
This is now an elementary trigonometric equation. So, recall how to solve it.

white adder
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Would you do inverse sine

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Which gives -90=(30(3-d)

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Then divide by 30

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3-d=-3

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d=6?

sturdy root
white adder
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+close

tidal locustBOT
# white adder +close
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# tidal locust

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