# Solving trigonometry problem in Wolfram|Alpha **URL:** \ **Category:** Questions\ **Tags:** wolfram-alpha\ **Created:** [February 22, 2021, 10:17pm UTC](https://community.wolfram.com/t/solving-trigonometry-problem-in-wolfram-alpha/17680 "2021-02-22T22:17:30Z")\ **Posts on this page:** 14\ **Page:** 1
**Author:** ![electricianid](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@electricianid](https://community.wolfram.com/u/electricianid)\ **Post date:** [February 22, 2021, 10:17pm UTC](https://community.wolfram.com/t/solving-trigonometry-problem-in-wolfram-alpha/17680/1 "2021-02-22T22:17:30Z")
Hello, I have the following wave.. 4 cos(3 theta)-6 sin(3 theta) …and express it in the following form… _R_sin(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 ---
**Author:** ![apozhitkov](https://avatars.discourse-cdn.com/v4/letter/a/71c47a/32.png) [@apozhitkov](https://community.wolfram.com/u/apozhitkov)\ **Post date:** [February 23, 2021, 12:10am UTC](https://community.wolfram.com/t/solving-trigonometry-problem-in-wolfram-alpha/17680/2 "2021-02-23T00:10:44Z")
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)](https://en.wikibooks.org/wiki/Trigonometry/Simplifying_a_sin%28x%29_+_b_cos%28x%29) ---
**Author:** ![electricianid](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@electricianid](https://community.wolfram.com/u/electricianid)\ **Post date:** [February 23, 2021, 7:42am UTC](https://community.wolfram.com/t/solving-trigonometry-problem-in-wolfram-alpha/17680/3 "2021-02-23T07:42:06Z")
Thanks for the link Alexander, but my question was about how to do this in Wolfram|Alpha. ---
**Author:** ![hansmilton](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/hansmilton/32/8656_2.png) [@hansmilton](https://community.wolfram.com/u/hansmilton)\ **Post date:** [February 23, 2021, 8:32am UTC](https://community.wolfram.com/t/solving-trigonometry-problem-in-wolfram-alpha/17680/4 "2021-02-23T08:32:25Z")
![7721Polarform.png](https://global.discourse-cdn.com/wolfram/original/3X/5/c/5c2cb0c5253792b0da87516e95206919f61262b2.png) **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) ---
**Author:** ![electricianid](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@electricianid](https://community.wolfram.com/u/electricianid)\ **Post date:** [February 23, 2021, 8:45am UTC](https://community.wolfram.com/t/solving-trigonometry-problem-in-wolfram-alpha/17680/5 "2021-02-23T08:45:23Z")
The problem asks for the answer in the form Rsin(3 theta + beta), is this possible and can the steps be shown? ---
**Author:** ![hdolhaine](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/hdolhaine/32/35924_2.png) [@hdolhaine](https://community.wolfram.com/u/hdolhaine)\ **Post date:** [February 23, 2021, 10:29am UTC](https://community.wolfram.com/t/solving-trigonometry-problem-in-wolfram-alpha/17680/6 "2021-02-23T10:29:58Z")
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 ---
**Author:** ![hdolhaine](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/hdolhaine/32/35924_2.png) [@hdolhaine](https://community.wolfram.com/u/hdolhaine)\ **Post date:** [February 23, 2021, 10:56am UTC](https://community.wolfram.com/t/solving-trigonometry-problem-in-wolfram-alpha/17680/7 "2021-02-23T10:56:47Z")
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 ``` ---
**Author:** ![electricianid](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@electricianid](https://community.wolfram.com/u/electricianid)\ **Post date:** [February 23, 2021, 11:15am UTC](https://community.wolfram.com/t/solving-trigonometry-problem-in-wolfram-alpha/17680/8 "2021-02-23T11:15:55Z")
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. ---
**Author:** ![hdolhaine](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/hdolhaine/32/35924_2.png) [@hdolhaine](https://community.wolfram.com/u/hdolhaine)\ **Post date:** [February 23, 2021, 11:39am UTC](https://community.wolfram.com/t/solving-trigonometry-problem-in-wolfram-alpha/17680/9 "2021-02-23T11:39:38Z")
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 ``` ---
**Author:** ![electricianid](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@electricianid](https://community.wolfram.com/u/electricianid)\ **Post date:** [February 23, 2021, 11:55am UTC](https://community.wolfram.com/t/solving-trigonometry-problem-in-wolfram-alpha/17680/10 "2021-02-23T11:55:51Z")
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 ---
**Author:** ![hdolhaine](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/hdolhaine/32/35924_2.png) [@hdolhaine](https://community.wolfram.com/u/hdolhaine)\ **Post date:** [February 23, 2021, 12:30pm UTC](https://community.wolfram.com/t/solving-trigonometry-problem-in-wolfram-alpha/17680/11 "2021-02-23T12:30:48Z")
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 ---
**Author:** ![electricianid](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@electricianid](https://community.wolfram.com/u/electricianid)\ **Post date:** [February 23, 2021, 12:36pm UTC](https://community.wolfram.com/t/solving-trigonometry-problem-in-wolfram-alpha/17680/12 "2021-02-23T12:36:12Z")
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? ---
**Author:** ![hdolhaine](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/hdolhaine/32/35924_2.png) [@hdolhaine](https://community.wolfram.com/u/hdolhaine)\ **Post date:** [February 23, 2021, 4:49pm UTC](https://community.wolfram.com/t/solving-trigonometry-problem-in-wolfram-alpha/17680/13 "2021-02-23T16:49:28Z")
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 > **[ArcTan: Arc tangent function—Wolfram Documentation](https://reference.wolfram.com/language/ref/ArcTan.html)** > > ArcTan\[z\] gives the arc tangent tan -1 (z) of the complex number z. ArcTan\[x, y\] gives the arc tangent of y/x, taking into account which quadrant the point (x, y) is in. > **[Manipulate: Create an Interactive User Interface—Wolfram Documentation](https://reference.wolfram.com/language/ref/Manipulate.html)** > > Manipulate\[expr, {u, umin, umax}\] generates a version of expr with controls added to allow interactive manipulation of the value of u. Manipulate\[expr, {u, umin, umax, du}\] allows the value of u to vary between umin and umax in steps du.... > **[Build a Manipulate—Wolfram Documentation](https://reference.wolfram.com/language/workflow/BuildAManipulate.html)** > > Make any expression interactive. 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. ---
**Author:** ![electricianid](https://avatars.discourse-cdn.com/v4/letter/e/c37758/32.png) [@electricianid](https://community.wolfram.com/u/electricianid)\ **Post date:** [February 23, 2021, 5:09pm UTC](https://community.wolfram.com/t/solving-trigonometry-problem-in-wolfram-alpha/17680/14 "2021-02-23T17:09:31Z")
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 . Regards, Ian