We'll solve the problem using 2
methods
First method:
4 sin x
= 3 cos x
sin x =( 3/4) cos
x
We'll divide by cos
x:
sinx/cosx = 3/4
But the
ratio sinx/cosx = tan x
tan x=
3/4
x = arctan (3/4) +
k*pi
The second
method:
We know that in a right triangle, due to
Pythagorean theorem,
sin^2 x + cos^2 x =
1
sin x = sqrt[1 - cos^2
(x)]
But, from hypothesis, sin x = (3/4)cos
x,so
(3/4)cos (x) = sqrt[1 - cos^2
(x)]
We'll square raise both
sides:
[(3/4)cos (x)]^2 = {sqrt[1 - cos^2
(x)]}^2
(9/16)cos^2 (x)= 1 - cos^2
(x)
(9/16)cos^2 (x )+ cos^2 (x) =
1
The least common denominator is 16, so we'll multiply
with 16, cos^2 (x) and the result will be:
(25/16)cos^2 (x)
= 1
cos^2 (x) = 16/25
cos x =
4/5
x = arccos (4/5) +
2*k*pi
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