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Reply 40
Ricki
Cheers!
:smile:


Here is the graphical solution.

--------------
Ricki
3cosx=2sin(x+60)
arctan(-?3 - ?9) = ?
? ? 78.07° etc.


The last theta should be negative 78.07 but this does not agree with graphical solution. I don't know why.



Here I plotted the tangent equation and this gives more solutions.

Reply 41
steve2005
The last theta should be negative 78.07 but this does not agree with graphical solution. I don't know why.



I knew that the root was θ = -78.07, but for some reason that did not give the correct solution when you sub it back into 3cosx=2sin(x+60) for some reason ..
but I noticed θ = 78.07 being a root, so I stated that.

It is weird, not to get θ = 78.07° graphically ... :eek:
Reply 42
Steve, that tangent equation doesn't give solutions to 3cosx = 2sin(x+60)

Graphically it doesn't work!

:smile:
Reply 43
Ricki
I knew that the root was ? = -78.07, but for some reason that did not give the correct solution when you sub it back into 3cosx=2sin(x+60) for some reason ..
but I noticed ? = 78.07 being a root, so I stated that.

It is weird, not to get ? = 78.07° graphically ... :eek:


I think there is a problem with squaring both sides, because when you square root later on you introduce extra illegal solutions. I think we have to use a different method. Like Rsin(theta + alpha)
Reply 44
steve2005
I think there is a problem with squaring both sides, because when you square root later on you introduce extra illegal solutions. I think we have to use a different method. Like Rsin(theta + alpha)


Ah right! that must be true, its always you have to be careful when squaring.

Well, my method does partially work, as the second solution was just θ = 360 - Ø where Ø was ≈ 78.07.

About putting it in the form Rsin(θ+Ø) , can you do this and show me, as I'm not familar with this yet!

:smile:
Reply 45
Ricki
Steve, that tangent equation doesn't give solutions to 3cosx = 2sin(x+60)

Graphically it doesn't work!

:smile:


Because the tangent equation does not produce the required solutions I conclude the tangent equation is wrong. I suspect this is because of illegal squaring earlier on.
Reply 46
Ricki
3cosx=2sin(x+60)
3cosx=2(sinxcos60+cosxsin60)
3cosx=2(sinx/2+√3cosx/2)
3cosx=sinx+√3cosx
9cos²x=(sinx+√3cosx)²
9cos²x = sin²x+2√3cosxsinx + 3cos²x
9cos²x = 1 - cos²x + 2√3cosxsinx + 3cos²x
7cos²x = 1 + 2√3cosxsinx
7 = 1/cos²x + 2√3sinx/cosx
7 = sec²x + 2√3tanx

Using sec²x = tan²x + 1 ...

7 = (tan²x + 1) + 2√3tanx
tan²x + 2√3tanx - 6 =0

sub t = tanx

+ 2√3t - 6 = 0
(t + √3)² - 3 - 6 = 0
t = -√3 ±√9

sub t = -√3 + √9 into t = tanx ...

arctan(-√3 + √9) = θ
θ ≈ 51.74° etc.

sub t = -√3 - √9 into t = tanx ...

arctan(-√3 - √9) = θ
θ ≈ 78.07° etc.


Yeah, the book gives 51.7 and 231.7 as the answers.
Reply 47
We should all be ashamed of ourselves here:redface: , we over compicated this question:

3cosx=2sin(x+60)
3cosx=2(sinxcos60+cosxsin60)
3cosx=2(sinx/2+√3cosx/2)
3cosx=sinx+√3cosx

Instead of squaring divide by cosx:
3=tanx+√3
tanx=3-√3
x=51.7
x=180+51.7=231.7
Reply 48
mala2k
We should all be ashamed of ourselves here:redface: , we over compicated this question:

3cosx=2sin(x+60)
3cosx=2(sinxcos60+cosxsin60)
3cosx=2(sinx/2+?3cosx/2)
3cosx=sinx+?3cosx

Instead of squaring divide by cosx:
3=tanx+?3
tanx=3-?3
x=51.7
x=180+51.7=231.7


Talk about over complicated...... this is using Rcos(x + alpha) ..
Reply 49
steve2005
Talk about over complicated...... this is using Rcos(x + alpha) ..


:smile: Suppose its just extra practice in the end, kudos for actually doing it that way!
Reply 50
mala2k
We should all be ashamed of ourselves here:redface: , we over compicated this question:

3cosx=2sin(x+60)
3cosx=2(sinxcos60+cosxsin60)
3cosx=2(sinx/2+√3cosx/2)
3cosx=sinx+√3cosx

Instead of squaring divide by cosx:
3=tanx+√3
tanx=3-√3
x=51.7
x=180+51.7=231.7


Oh my god, that would've been so much easier! :eek:
Reply 51
mala2k
We should all be ashamed of ourselves here:redface: , we over compicated this question:

3cosx=2sin(x+60)
3cosx=2(sinxcos60+cosxsin60)
3cosx=2(sinx/2+√3cosx/2)
3cosx=sinx+√3cosx

Instead of squaring divide by cosx:
3=tanx+√3
tanx=3-√3
x=51.7
x=180+51.7=231.7


I have my reason, of being in a hurry, so was rushing things! :redface:

Nice elegant solution. :smile: