what is angle if sin angle=sin 4angle?show general solution

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sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You should come up with the substitution angle=`alpha ` such that:

`sin alpha = sin 4 alpha`

You may use two methods to find alpha. I suggest you to solve using the following method since it does not involve the use of so many trigonometric formulas.

`alpha = (-1)^n*sin^(-1)(sin 4 alpha) + n*pi`

`alpha = (-1)^n*4 alpha + n*pi`

If n is even, then `alpha = 4alpha + 2npi =gt -3alpha = 2npi`

`alpha = -(2npi)/3`

If n is odd, then `alpha = -4alpha + 2npi + pi=gt 5alpha = 2npi+ pi`

`alpha = (2n+1)*pi/5`

Hence, evaluating general solutions to trigonometric equation yields `alpha = -(2npi)/3`  and `alpha = (2n+1)*pi/5` .

aneesh97's profile pic

aneesh97 | Student, Grade 9 | (Level 1) eNoter

Posted on

i guess the value of the angle is 0

therefore sin 0= sin 4*0

            =>sin 0=sin 0

 

Hope it helps... :)

minhthien94's profile pic

minhthien94 | Student, Undergraduate | (Level 1) eNoter

Posted on

sin(4x) = sin(x)

sin(4x) - sin(x) = 0

2cos(5x/2) . sin(3x/2) = 0

cos(5x/2) = 0 or sin(3x/2) = 0

For cos(5x/2) = 0

      5x/2 = pi/2 + n.pi

      x = pi/5 + 2n.pi/5

For sin(3x/2) = 0

      3x/2 = n.pi

      x = 2n.pi/3

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