What will be the solution of Sin(3x) = 1/2 in the interval (pi, 2pi)

Asked by anushankdagar95 | 23rd Oct, 2019, 08:55: AM

Expert Answer:

sin(3x) = 1/2 = sin [2nπ + (π/6)]= sin [(12n+1)π/6]
 
3x = (12n+1)π/6   or   x = (12n+1)π/18 ..................(1)
 
if we need x in the interval ( π , 2π ) , n =2 in eqn. (1),  we get,  x = (25/18)π
 
we have,  sin[ (2n+1)π - θ ] = sinθ
 
hence,  sin[ (2n+1) π - (π/6) ] = sin [ 2n π + (5/6)π ] = (1/2)
 
hence 3x = 2n π + (5/6)π   or  x =  (12n+5)π/18 ..................(2)
 
if we need x in the interval ( π , 2π ) , n =2 in eqn. (2), we get x = (29/18)π
 
Hence we get solution,  x = (25/18)π   or   (29/18)π   ..........................(3)

 

 
 

Answered by Thiyagarajan K | 23rd Oct, 2019, 09:39: AM

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