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Trig Equations help...?
sin4x + 2sin2x = 0
I have to find all exact solutions. How should i start?? thanks
Nothing is being raised to any power.
Just
Sin(4x) + 2 Sin(2x) =0
3 Answers
- huetLv 41 decade agoFavorite Answer
= 2Sin2xCos2x +2Sin2x =0 because sin4x=2sin2xcos2x
2sin2x(cos2x+1) =0 the following can happen:
sin2x=0 => 2x=0, Pi, 2Pi or x=0, Pi/2, Pi
cos2x+1 = 0 => cos2x=-1 => 2x=Pi => x=Pi/2
Then all solutions are: x=0, Pi/2, Pi
- grunfeldLv 71 decade ago
is this sin^4 x + 2 sin^2 x = 0 or sin^4 x + 2 sin 2x = 0 or sin 4x + 2 sin^2 x = 0 or sin 4x + 2 sin 2x = 0 ??
Source(s): my brain - Amar SoniLv 71 decade ago
sin (4x) + 2 sin (2x) = 0
because sin (2theta) = 2 sin (theta). cos (theta) , this is an identity of trignometry
{2sin(2x)* cos(2x)} +2 sin( 2x)= 0
2 sin(2x){cos (2x) + 1}=0
Therefore
sin 2(x) =0 and cos (2x) = -1
when sin(2x) = 0
2x = 0,180, 360, 540 .......................degrees
x = 0,90,180, 270, 360..............degrees.........................Ans
when
cos(2x) = -1
2x = 180 degrees and 540 degrees
x = 90, 270.............degrees..................Ans
