A community for students.
Here's the question you clicked on:
 0 viewing
BluFoot
 2 years ago
How can I simplify sin^5x? I need to write it in terms of sinx, sin(3x) and sin(5x).
BluFoot
 2 years ago
How can I simplify sin^5x? I need to write it in terms of sinx, sin(3x) and sin(5x).

This Question is Closed

BluFoot
 2 years ago
Best ResponseYou've already chosen the best response.0Hahaha I know how to use wolframalpha! I don't how to get there :P

henpen
 2 years ago
Best ResponseYou've already chosen the best response.0Use Euler's formula. You know it?

BluFoot
 2 years ago
Best ResponseYou've already chosen the best response.0No, I'll look into it though and post back.

henpen
 2 years ago
Best ResponseYou've already chosen the best response.0\[\Im((e^{i\theta})^5)=\Im(e^{i5\theta})\]

BluFoot
 2 years ago
Best ResponseYou've already chosen the best response.0Definitely don't know that! This is a linear algebra course, the original question is find the coordinate vector for sin^5(x) from the basis {sinx,sin3x,sin5x}. So far, I've been trying to use addition rules to simplify them. sin(3x)=(sin2x+x) etc. But it's taking forever, there must be a better way!

henpen
 2 years ago
Best ResponseYou've already chosen the best response.0\[e^{ix}=\cos(x)+\sqrt{1}\sin(x)\] \[(e^{ix})^2=(\cos(x)+\sqrt{1}\sin(x))^2=cos^2(x)sin^2(x)+2\sqrt{1}cos(x)sin(x)\] \[(e^{ix})^2=e^{i2x}=cos(2x)+\sqrt{1}sin(2x)\]Use the fact that if you have \[f(x)+\sqrt{1}g(x)=h(x)+\sqrt{1}p(x)\]Then this MUST be true: \[f(x)=h(x)\] and \[g(x)=p(x)\]

henpen
 2 years ago
Best ResponseYou've already chosen the best response.0Use for\[e^{i5x}=(e^{ix})^5\]The \[\Im\]bit just means 'remove all the things that do not have a coefficient of \[\sqrt{1}\] in front of them.

henpen
 2 years ago
Best ResponseYou've already chosen the best response.0\[\sqrt{1}=i=\text{ imaginary number } \] My method may look tricky, but it's MUCH simpler

henpen
 2 years ago
Best ResponseYou've already chosen the best response.0http://betterexplained.com/articles/avisualintuitiveguidetoimaginarynumbers/

whatisthequestion
 2 years ago
Best ResponseYou've already chosen the best response.0@henpen I think the equations you are using are beyond the level o math @blufoot is at I believe he is suppose to be using the base trig identites

henpen
 2 years ago
Best ResponseYou've already chosen the best response.0Fair enough, but it's always useful to know where the base identities come from. You help I need to sleep.

henpen
 2 years ago
Best ResponseYou've already chosen the best response.0Blufoot, you're on the right track, use sin(a+b)=sinacosb+sinbcosa

BluFoot
 2 years ago
Best ResponseYou've already chosen the best response.0Hey that's ok this is interesting! I remember learning a bit about imaginary numbers back in high school, but I don't see how it leads me to solving for sin(5x) :P I guess I'll just have to use the identities :( sin(3x) is easy, but sin(5x) takes forever because it's sin(3x+2x) which is cos(2x)sin(3x)+sin(2x)cos(3x)... So I need cos(3x) also and a ton of simplifying... I guess I'll give in to wolframalpha!

whatisthequestion
 2 years ago
Best ResponseYou've already chosen the best response.0wait is this \[\sin ^{5}x\] or \[\sin(5x)\]

BluFoot
 2 years ago
Best ResponseYou've already chosen the best response.0Oh, either one, really. I'm trying to write sin^5x in terms of the other 3. I'm not sure if sin^5x is an easier one to simplify? Couldn't find a rule for that one...

whatisthequestion
 2 years ago
Best ResponseYou've already chosen the best response.0there is a rule that may help with the load if you can figure out how to deal with the cos(x) its \[\sin ^{2}(x)=\frac{ 1\cos(2x) }{ 2 }\]

whatisthequestion
 2 years ago
Best ResponseYou've already chosen the best response.0which I would think means \[\sin ^{5}(x)=\frac{ 1\cos(5x) }{ 5 }\] but I could also be horribly mistaken in that conclusion

whatisthequestion
 2 years ago
Best ResponseYou've already chosen the best response.0I am sorry but I actually have got to go bye
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.