3sinx-2cosx=o; find G s
huh? HUH?
Do you want to find solutions to the equation
3sinx - 2cosx = 0 ?
since 3^2+2^2 = 13, this is equivalent to
√13 (3/√13 sinx - 2/√13 cosx) = 0
Now, let y be the angle such that cosy = 3/√13. Then siny = 2/√13. Now you have
√13 (sinx cosy - cosx siny) = 0
√13 sin(x-y) = 0
So, x-y=0 or x-y = π
That is, x-y = kπ for any integer k.
Thus, x = kπ + arcsin(2/√13)
OR
3 sin x - 2 cos x = 0
3 sin x = 2 cos x
3 sin x / cos x = 2
3 tan x = 2
tan x = 2 / 3
x = k π + tan⁻¹ ( 2 / 3 )
x = k π + arctan ( 2 / 3 )
k π + arctan ( 2 / 3 ) and x = k π + arcsin ( 2 / √13 )
is the same solution is written in a different way.
much simpler, Bosnian. I missed that one, fer shure!
To find the value of G, given the equation 3sin(x) - 2cos(x) = 0, we can use the trigonometric identities to rewrite the equation in terms of a single trigonometric function.
First, we can multiply the entire equation by 1/√(sin^2(x) + cos^2(x)) (which is equal to 1):
(3/√(sin^2(x) + cos^2(x)))sin(x) - (2/√(sin^2(x) + cos^2(x)))cos(x) = 0
Next, we can use the identity sin^2(x) + cos^2(x) = 1:
(3/√1)sin(x) - (2/√1)cos(x) = 0
Simplifying further, we have:
3sin(x) - 2cos(x) = 0
Now, we can rewrite the equation in terms of tangent (tan(x)):
3sin(x) - 2cos(x) = 0
3sin(x) = 2cos(x)
(sin(x))/cos(x) = 2/3
tan(x) = 2/3
Now that we have the equation in terms of tan(x), we can find the value of x by taking the inverse tangent (also known as arctan) of both sides of the equation:
arctan(tan(x)) = arctan(2/3)
x = arctan(2/3)
So, G = arctan(2/3).