Hello,
I have the following wave..
4 cos(3 theta)-6 sin(3 theta)
...and express it in the following form...
Rsin(3 theta + beta)
I'd be grateful if anyone can explain how to do this in Wolfram|Alpha?
(BTW - I have typed theta and beta as I don't know how to type the symbols.)
Regards, Ian
Thanks Hans, I'll take a look at Mathematica when time permits. I'm going to take a break from Wolfram|Alpha for a while as it's slowing me down and I need to move on with my course .
I don't know anything about Symbolab. I think Mathematica is a good choice. Documentation is availabel. sometimes not satisfactory, but in general good.
Look for example at
https://reference.wolfram.com/language/ref/ArcTan.html https://reference.wolfram.com/language/ref/Manipulate.html https://reference.wolfram.com/language/workflow/BuildAManipulate.html
I am not quite sure but I think you can download a testversion of Mathematica without costs for one month. But I do not know that.
Do you think Mathmatica is a better choice, is there documentation available?
I've heard good things about Symbolab, do you think this would be a good option?
Ok. Pity. Perhaps you should consider to switch to Mathematica.
I typed
- 6/Cos[ArcTan[-2/3]] Sin[x + ArcTan[-2/3]]
into Wolfram Alpha and got everything you wanted.
x is 3 theta and ArcTan[-2/3] is your beta
Too much for me Hans.
I think WA can only be used by people who don't really need it.
I've tried my best but can't see how it can help me
Ok, I know next to nothing about Wolfram|Alpha.
But there is an analytical solution as well, obtained with Mathematica, and I think, you could get it with Wolfram|Alpha as well.
Try
aa = -1/Cos[ArcTan[-2/3]] 6 aa Sin[x + ArcTan[-2/3]] // TrigExpand
Hi Hans,
I've tried both suggestions in Wolfram|Alpha. The first returned a definition of the word 'manipulate' and the second described a table and displayed a photo of a coffee table. I'm probably doing something wrong but what you've suggested is quite complicated and requires special knowledge that I neither have nor know where to find. I thought Wolfram|Alpha would be more straightforward than this given that no documentation is provided. I don't think it will ever be of use to me, which is disappointing as I've spent quite a lot of money on the subscription.
Or do this
data = Table[{th, 4 Cos[3 th] - 6 Sin[3 th]}, {th, 0, 2 Pi, .1}]; fit = NonlinearModelFit[ data, f Sin[3 th + b], {{f, 7.16}, {b, 2.16}}, th] // Normal Table[ {4 Cos[3 th] - 6 Sin[3 th], fit}, {th, 0, 2 Pi, .05}]; % // TableForm
What about this?
Manipulate[ Plot[ {4 Cos[3 th] - 6 Sin[3 th], f Sin[3 th + b]}, {th, 0, 3 Pi}, PlotStyle -> {Blue, {Thick, Red}}], {f, 0, 10}, {b, 0, 2 Pi}]
Look at f = 7.16 and b = 2.613
The problem asks for the answer in the form Rsin(3 theta + beta), is this possible and can the steps be shown?
EDIT :
$R=-2 \sqrt{13}$
$\beta =-\tan ^{-1}\left(\frac{2}{3}\right)$
A negative R (radius) looks strange, but the expression is equal to: $$2 \sqrt{13} \sin \left(\tan ^{-1}\left(\frac{2}{3}\right)-3 \theta \right)$$
Thanks for the link Alexander, but my question was about how to do this in Wolfram|Alpha.
This exactly shows how to solve this problem. I was wondering about it for a while myself and a few years ago found that solution:
Trigonometry/Simplifying a sin(x) + b cos(x)