0
OK. Let's give it a whirl:
2 cos2 + sin - 1 = 0
Remember that cos2 = 1 - sin2 . Then, substitute that in the given equation
to see whether there appears to be any chance that it makes life easier:
2 (1 - sin2) + sin - 1 = 0
Eliminate parentheses :
2 - 2 sin2 + sin - 1 = 0
Combine like terms, clean it up, and multiply each side by -1 :
2 sin2 - sin - 1 = 0
This looks factorable:
(2 sin + 1) (sin - 1) = 0
Now we have it within our grasp.
2 sin(x) = 0
sin(x) = 0
x = + or - N pi
sin(x) - 1 = 0
sin(x) = 1
x = pi/2 + 2N pi
'x' is 90 degrees, and every multiple of 180 degrees.
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What is the value of sinX wrt cosX?
sin(x) = sqrt[ 1 - cos2(x) ]
What is the minimum value that the graph of y equals sinx assumes?
-1
Integral of sin 2x divided by 1 plus cosine squared x?
3
What is the derivative of 1 divided by sinx?
y=1/sinxy'=(sinx*d/dx(1)-1*d/dx(sinx))/(sin2x)y'=(sinx*0-1(cosx))/(sin2x)y'=(-cosx)/(sin2x)y'=-(cosx/sinx)*(1/sinx)y'=-cotx*cscx
What is sin 3x in terms of sin x?
given the identity sin(x+y)=sinx cosy + siny cosxsin2x = 2 sinx cosx andsin(2(x)+x) = sin 2x cos x + sinx cos 2xusing the last two identities givessin3x= 2 sinx cosx cosx + sinx cos2xfactoring the sinx we havesin3x = sinx(2cosx cosx+cos2x)which satisfies the requirement.However, we can simplify further since cos 2x = cosx cosx - sinx sinx (a well known identity)sin3x = sinx (2cosx cosx +cosx cosx - sinx sinx)so sin3x= sinx(3cosx cosx - sinx sinx)or sin 3x = 3.cos²x.sinx - sin³x* * * * *Good, but not good enough. The answer was required in terms of sin, not a mixture of sinx and cosx. Easily recitified, though, since cos²x = 1 - sin²xTherefore sin3x = 3*(1-sin²x)*sinx - sin³x= 3sinx - 3sin³x - sin³x= 3sinx - 4sin³x
