Question 1093922: Given: 4 sin A = 3 cos A
Find:
1. Sin A
2. Cos A
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you have 4 * sin(a) = 3 * cos(a)
solve for sin(a) to get sin(a) = 3/4 * cos(a).
solve for cos(a) to get cos(a) = 4/3 * sin(a).
solve for tan(a) to get tan(a) = sin(a) / cos(a) = 3/4.
you have a 3,4,5 triangle.
one of your acute angles has 3 as the adjacent side and 4 as the opposite side.
the other of your acute angles has 3 as the opposite side and 4 as the adjacent side.
the angle that has 3 as the opposite side and 4 as the adjacent side is your angle of interest.
we'll call that angle(a).
tan(a) = 3/4.
a = arctan(3/4) = 36.86989765 degrees.
using that value for the angle, we get:
sin(36.86989765) = .6
cos(36.86989765) = .8
tan(36.86989765 = .75
we have:
sin(a) = 3/4 * cos(a) = 3/4 * .8 = .6
cos(a) = 4/3 * sin(a) = 4/3 * .6 = .8
solution checks out.
not sure what you needed, but:
sin(a) = .6
cos(a) = .8
sin(a) = 3/4 * cos(a) = 3/4 .8 = .6
cos(a) = 4/3 * sin(a) = 3/4 * .6 = .8
tan(a) = 3/4
a = 36.86989765
without solving for the angle, you would find the hypotenuse of the right triangle by using pythagorus formula of c^2 = a^2 + b^2 where c is the hypotenuse and a is one leg and b is the other leg.
you would get hypotenuse = 5.
it's a 3,4,5 triangle with the angle you are looking for being opposite the side of length 3 and adjacent to the side of length 4.
tan(a) = opp/adj = 3/4
sin(a) = opp/hyp = 3/5 = .6
cos(a) = adj/hyp = 4/5 = .8
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