Thursday

October 23, 2014

October 23, 2014

Posted by **carmen** on Friday, August 24, 2012 at 8:49am.

- maths -
**Steve**, Friday, August 24, 2012 at 10:39amThis 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.

**Answer this Question**

**Related Questions**

Math - sin5x=cosx, find the general solutions for this please =)

maths - hey, i would really appreciate some help solving for x when: sin2x=cosx ...

maths - (Sin^3x-cos^3x)/(sinx-cosx) – cosx/sqrt(1+cot^2x)-2tanxcotx=-1 where x&#...

Math - How many solutions does the equation cosx + 1/2 = 1 have for 0<x<...

TRIGONOMETRY - Can someone please show me step by step solutions? I'd appreciate...

trig - it says solve for all real solutions, compute inverse functions to 4 ...

Maths - Solve this equation fo rx in the interval 0<=x<=360 3sinxtanx=8 I ...

Calculus - Find the following limits algebraically or explain why they don’t ...

Precalculus - Please help!!!!!!!!!!! Find all solutions to the equation in the ...

Pre-Calc - Trigonometric Identities Prove: (tanx + secx -1)/(tanx - secx + 1)= ...