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Aaah! new group for trigonometry :)
Let me start this by asking to expand sin 5x in powers of sin x.
Only for those who have started learning trigonometry and never tried this.
Those who already know how to, can give other methods, not discussed here, later.
 one year ago
 one year ago
Aaah! new group for trigonometry :) Let me start this by asking to expand sin 5x in powers of sin x. Only for those who have started learning trigonometry and never tried this. Those who already know how to, can give other methods, not discussed here, later.
 one year ago
 one year ago

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lgbasalloteBest ResponseYou've already chosen the best response.0
using the new groups is fun, isn't it?
 one year ago

hartnnBest ResponseYou've already chosen the best response.4
its just the beginning...... Another similar exercise would be to write sin^5 x in terms of sin5x,sin4x,...
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
...i never really learned these stuffs...all i know are the basics of trigonometry....
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
but i do have an idea how to do it......but it's brute force.....is there a shorter way?
 one year ago

hartnnBest ResponseYou've already chosen the best response.4
there are few ways i am aware of...idk what do u mean by brute force here....u can try to expand here,if u want.
 one year ago

lgbasalloteBest ResponseYou've already chosen the best response.0
my idea is using sin (2x) over and over
 one year ago

joemath314159Best ResponseYou've already chosen the best response.3
hmm...the first way that pops into my mind is using:\[e^{ix}=\cos(x)+i\sin(x)\]and being a little clever.
 one year ago

joemath314159Best ResponseYou've already chosen the best response.3
Noting that sin(5x)= Im(cos(5x)+isin(5x))=Im(e^(5ix))=Im((e^ix)^5) =Im((cos(x)+isin(x))^5). So basically, if you see what the imaginary part of:\[(\cos(x)+i \sin(x))^5\]is, you will have a formula for sin(5x).
 one year ago

hartnnBest ResponseYou've already chosen the best response.4
nice! lets see how new learners try it... maybe they don't even know that e^{ix} identity
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
I do know that formula made by Euler, but I didn't know we could apply that here. :P
 one year ago

hartnnBest ResponseYou've already chosen the best response.4
u can try it parth.... maybe @mathslover also wanna try this....
 one year ago

joemath314159Best ResponseYou've already chosen the best response.3
Here is an example of using Euler's formula to show that:\[\cos(2x)=\cos^2(x)\sin^2(x)\]\[\sin(2x)=2\sin(x)\cos(x)\]
 one year ago

mathsloverBest ResponseYou've already chosen the best response.0
Yeah , it is great to see the new pattern : @hartnn can you explain how to do it?
 one year ago
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