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Mathematics Clinic => Grade 9 Mathematics => Topic started by: formula1 on Oct 4, 2013

Title: I need to find an angle, x, but the formula has sin x times cos x, what do I do?
Post by: formula1 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??

Title: I need to find an angle, x, but the formula has sin x times cos x, what do I do?
Post by: clippers! on Oct 4, 2013

Q/(pgH) = cosxsinx
2Q/(pgH) = 2cosxsinx
2Q/(pgH) = sin(2x)
2x = arcsin[2Q/(pgH)]
x = .5arcsin[2Q/(pgH)]

Title: I need to find an angle, x, but the formula has sin x times cos x, what do I do?
Post by: geoffrey 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

Title: I need to find an angle, x, but the formula has sin x times cos x, what do I do?
Post by: aero 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.