SOLUTION: Given: 4 sin A = 3 cos A Find: 1. Sin A 2. Cos A

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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