Hi friends, please solve the following problem and post the solution ? If Sin (3x) = (root 10) / 8 then Sin x = ?

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Sin(3x)=(root10)/8 Squaring both sides (Sin^2)3x=10/64=5/32 (1-cos6x)/2=5/32 1-cos6x=5/16 1-5/16=cos6x Cos3x2x=11/16 4(cos^3)2x-3cos2x=11/16 64(cos^3)2x-48cos2x_11=0 For cos2x =-1/4 the equation satisfies So cos2x=-1/4 is one of the solution You try to get the other2 solutions . They are...
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Sin(3x)=(root10)/8 Squaring both sides (Sin^2)3x=10/64=5/32 (1-cos6x)/2=5/32 1-cos6x=5/16 1-5/16=cos6x Cos3x2x=11/16 4(cos^3)2x-3cos2x=11/16 64(cos^3)2x-48cos2x_11=0 For cos2x=-1/4 the equation satisfies So cos2x=-1/4 is one of the solution You try to get the other2 solutions . They are >1 and<-1 for cosx the range lies between -1and1 Socos2x=-1/4 1-2(sin^2)x=-1/4 1+1/4=2{sin^2)x (Sin^2)x=5/8 Sinx=root(5/8)or. -root(5/8) Sin=root10/4 or. -root10/4 read less
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sin 3x=root10/8 3X= sin-1 Root 10/8 X=1/3 sin -1 root 10/8 X= 23.28 sin X = 0.39
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Math Educator for Std.11th ,12th , Engineering Entrance and Degree Level with 11+ Years Experience

Sin(3x)=(root10) / 8 (3x)=inverse Sin (root10/8) (3x)=23.284 (x) = 23.284 / 3 (x) = 7.761 then sin x = 0.135
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Dedicated, well qualified mathematicians with a passion to nurture young minds in Mathematics and Physics

use the formula for sin 3A and solve the cubic in sin x
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Trainer

3x = Arc Sin(root10/8) = 23.284 x = 1/3( 23.284) = 7.76 Sin (7.76) =0.135 approximately.
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SME in Mathematics & Statistics

sin x = 0.135
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Tutor

As it is a cubic equation it has 3 solutions. sin x = 0.791, -0.926, 0.135
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Tution for Mathematics

solve like this... Sin(3x)=root10/8 (3x)=inverse of Sin (root10/8) you will get (3x)=23.2837 (x) = 23.2837/3 (x) = 7.76124 now take sin of x you will get = 0.13504
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Tutor

sinx = 0.135
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Tutor

0.1350
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