Asked by carmen
find general solutions for sin5x=cosx
Answers
Answered by
Steve
This is pointless. There are lots of solutions, but they are nasty, and really don't provide any insights.
sin(5x) = sin^5 + 5sin*cos^4 - 10sin^3cos^2
= sin*(1-cos^2)^2 + 5sincos^4 - 10sin(1-cos^2)cos^2
= sin(12cos^4 - 12cos^2 + 1)
so, you end up trying to solve
sin(x) (12cos^4(x) - 12cos^2(x) + 1) = cos(x)
No way to get rid of the sin except to square both sides, and then you wind up with
144cos^10(x) - 432cos^8(x) + 456cos^6(x) - 192cos^4(x) + 26cos^2(x) - 1 = 0
So, you have to solve a 5th-degree polynomial in cos^2(x), then try to eliminate possible spurious solutions.
Good freakin' luck!
Visit wolframalpha.com to see the solution and the graphs.
Just type in "solve sin 5x = cos x"
Not sure what the point is to this exercise.
sin(5x) = sin^5 + 5sin*cos^4 - 10sin^3cos^2
= sin*(1-cos^2)^2 + 5sincos^4 - 10sin(1-cos^2)cos^2
= sin(12cos^4 - 12cos^2 + 1)
so, you end up trying to solve
sin(x) (12cos^4(x) - 12cos^2(x) + 1) = cos(x)
No way to get rid of the sin except to square both sides, and then you wind up with
144cos^10(x) - 432cos^8(x) + 456cos^6(x) - 192cos^4(x) + 26cos^2(x) - 1 = 0
So, you have to solve a 5th-degree polynomial in cos^2(x), then try to eliminate possible spurious solutions.
Good freakin' luck!
Visit wolframalpha.com to see the solution and the graphs.
Just type in "solve sin 5x = cos x"
Not sure what the point is to this exercise.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.