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Author Question: I need to find an angle, x, but the formula has sin x times cos x, what do I do? (Read 1608 times)

formula1

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on: Oct 4, 2013
I have the formula Q = pgH cos x sin x
and I need to find the angle x. How do I rearrange the formula and how do I put it into my calculator??


clippers!

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Reply #1 on: Oct 4, 2013
Q/(pgH) = cosxsinx
2Q/(pgH) = 2cosxsinx
2Q/(pgH) = sin(2x)
2x = arcsin[2Q/(pgH)]
x = .5arcsin[2Q/(pgH)]


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geoffrey

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Reply #2 on: Oct 4, 2013
Q = pgH * cos(x) * sin(x)
Q / pgH = cos(x) * sin(x)
cos(x) * sin(x) = Q / pgH

sin(2x) = 2sin(x)cos(x)
sin(2x) / 2 = 2sin(x)cos(x) / 2
sin(2x) / 2 = sin(x)cos(x)

cos(x) * sin(x) = Q / pgH
sin(2x) / 2 = Q / pgH
sin(2x) = 2Q / pgH

2x = sin^-1(2Q / pgH)
x = sin^-1(2Q / pgH) / 2

sin^-1(2Q / pgH) means sin inverse of 2Q / pgH


aero

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Reply #3 on: Oct 4, 2013
Write Q = pgH cos x sin x,  as  2Q/pgH  = 2cos x sin x

 => 2Q/pgH  = sin 2x

 => 2x = sin^-1 (2Q/pgH)

 => x = (1/2) sin^-1 (2Q/pgH)

 Now you can find x by putting it in your calculator.


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