Use an expression for sin &#x2061;<!-- ⁡ --> ( 5 &#x03

deformere692qr 2022-05-09 Answered
Use an expression for sin ( 5 θ ) sin ( θ ) to find the roots of the equation x 4 3 x 2 + 1 = 0 in trigonometric form
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

rynosluv101swv2s
Answered 2022-05-10 Author has 19 answers
HINT:
Using Prosthaphaeresis Formula,
sin 5 x sin x = 2 sin 2 x cos 3 x = 4 sin x cos x cos 3 x
If sin x 0 ,,
sin 5 x sin x 1 = 4 cos x cos 3 x = 4 cos x ( 4 cos 3 x 3 cos x ) = ( 4 cos 2 x ) 2 3 ( 4 cos 2 x )
OR replace sin 2 x with 1 cos 2 x in your
5 cos 4 x 10 cos 2 x sin 2 x + sin 4 x
Now if sin 5 x = 0 , 5 x = n π where n is any integer
x = n π 5 where n 0 , ± 1 , ± 2 ( mod 5 )
So, the roots of sin 5 x sin x = 0 x = n π 5 where n ± 1 , ± 2 ( mod 5 )
But
sin 5 x sin x = ( 4 cos 2 x ) 2 3 ( 4 cos 2 x ) + 1
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more