How do I solve for x in this trig problem?

Question

Help! I am completely stumped...

4sin^2(3x)=3

Answer 1

4sin^2(3x) = 3
or sin^2(3x) + 3 sin^2(3x) = 3
or sin^2(3x) = 3[1 - sin^2(3x) ]
or sin^2(3x) = 3 cos^2(3x)
or tan^2(3x) = 3
or tan 3x = sqrt(3)

or 3x = 60 degrees or x = 20 degrees

Answer 2

you divide the two sides by 4

sin^2(3x) = 3/4 = 0.75

sin3x = 0.886 sin3x = -.866

3x =60 or 120 x=20 or x=40

3x=300 x=100 3x = 240 x= 80

Answer 3

Put an x in the inital answer which would give you 3x, then divide both by 3 and it gives you x. Then since both x's are equivalent you can use guess and check to figure out the rest.

Ex.
4sin^2(3x)=3
4sin^2(3x)=3x
4sin^2(x)=x

...you do the rest i dont kno sin, cos, and tan off hand.

Answer 4

sin^2(3x)=3/4
sin3x=squared root 3 /2
3x=2kpi+pi/3 ==> x=2/3kpi+pi/9
and 3x=2kpi+pi-pi/3 ==>
x=2/3kpi+pi/3-pi/9=2/3pi(k+1)=2/3k'pi

sin3x=-squared root 3 /2
3x=2kpi-pi/3 ==>x=2/3kpi-pi/9
3x=2kpi+pi+pi/3 ==> x=2/3kpi+pi/3+pi/9=2/3kpi+4/9pi

Answer 5

Step by step, use algebra to isolate x.

(sin3x)^2 = 3/4.

sin(3x) = [root(3/4)].

3x = arcsine[root(3/4)].

x = {arcsin[root(3/4)]}/3.

x = (60degree)/3 = 20degree

Answer 6

sin (3x) = +/- sqrt(3) / 2
<=> 3x = +/- pi/6 or +/- 5/6*pi
<=> x= pi/18 or x= -pi/18 or x=5pi/18 or x= -5pi/18

Answer 7

i don't know if this is completely correct and i don't know maths in english, but i'll try .. :D
sin^2(3x)=3/4 => sin(3x)=(square_root of 3)/2 => 3x=60 degrees => x=20
i think it''s correct
u're welcome :D

Answer 8

sin^2(3x)=3/4
sin(3x)=+√3 /2 & -√3/2
sin(3x)=sin(pi/3) & sin(3x)=-sin(pi/3)
3x=2kpi+(pi/3),
3x=2kpi+pi-(pi/3)
&3x=2kpi+(-pi/3),
3x=2kpi+pi+pi/3

x=(2kpi)/3+(pi/9),
x=(2kpi)/3+(2pi/9)
&
x=(2kpi)/3-(pi/9),
x=(2kpi)/3+(4pi/9)