If your expression mean:
4+29sin(x)=12cos^2(x)
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solve 4+29sin(x)=12cos^2(x)
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4+29sin=12cos^2
How do you determine this
4 answers
Remark:
cos ^ 2 ( x ) = 1 - sin ^ 2 ( x )
12 cos ^ 2 ( x )= 12 [ 1 - sin ^ 2 ( x ) ] =
12 - 12 sin ^ 2 ( x )
29 sin ( x ) - 12 cos ^ 2 ( x ) + 4 =
29 sin ( x ) - [ 12 - 12 sin ^ 2 ( x ) ] + 4 =
29 sin ( x ) - 12 + 12 sin ^ 2 ( x ) + 4
= 29 sin ( x ) - 8 + 12 sin ^ 2 ( x ) =
12 sin ^ 2 ( x ) + 29 sin ( x ) - 8
cos ^ 2 ( x ) = 1 - sin ^ 2 ( x )
12 cos ^ 2 ( x )= 12 [ 1 - sin ^ 2 ( x ) ] =
12 - 12 sin ^ 2 ( x )
29 sin ( x ) - 12 cos ^ 2 ( x ) + 4 =
29 sin ( x ) - [ 12 - 12 sin ^ 2 ( x ) ] + 4 =
29 sin ( x ) - 12 + 12 sin ^ 2 ( x ) + 4
= 29 sin ( x ) - 8 + 12 sin ^ 2 ( x ) =
12 sin ^ 2 ( x ) + 29 sin ( x ) - 8
When I solved this out I got x=-32/12 and x=1/4. Is this right?
Not x = .... but rather sinx = -32/12 or sinx = 1/4
Picking up from where Bosnian left off
12sin^2 x+ 29sinx - 8 = 0
(4sinx - 1)(3sinx + 8) = 0
sinx = 1/4 or sinx = -8/3, but sinx has to be between -1 and 1, so the last part is undefined
sinx = 1/4, so
x = 14.48° or 165.52°
if you want radians, set your calculator to RAD
and find arcsin (.25)
Picking up from where Bosnian left off
12sin^2 x+ 29sinx - 8 = 0
(4sinx - 1)(3sinx + 8) = 0
sinx = 1/4 or sinx = -8/3, but sinx has to be between -1 and 1, so the last part is undefined
sinx = 1/4, so
x = 14.48° or 165.52°
if you want radians, set your calculator to RAD
and find arcsin (.25)