how can i solve for x given this?? pls. show detailed solution..just can't figure it out.thanks in advance!
6cosx+3cos35cosx-3sin35sinX=7cosx
6*Cos x + 2.46*Cos x - 1.72*sin x = 7*Cos x.
8.46*Cos x - 1.72*sin x = 7*Cos x.
8.46*Cos x - 7*Cos x = 1.72*sin x.
1.46*Cos x = 1.72*sin x.
Divide by Cos x:
1.72*sin x/Cos x = 1.46.
Replace sin x/Cos x with Tan x:
1.72*Tan x = 1.46.
Tan x = 1.46/1.72 = 0.84848.
X = 40.3 Degrees.
To solve for x in the given equation, we will simplify and isolate the terms containing x on one side of the equation. Let's break it down step by step:
1. Distribute the cosine and sine terms using the trigonometric identity: cos(A + B) = cos(A)cos(B) - sin(A)sin(B).
6cos(x) + 3cos(35)cos(x) - 3sin(35)sin(x) = 7cos(x)
2. Combine the like terms on the left side.
(6 + 3cos(35))cos(x) - 3sin(35)sin(x) = 7cos(x)
3. Subtract 7cos(x) from both sides of the equation to isolate the terms containing x on one side.
(6 + 3cos(35))cos(x) - 7cos(x) - 3sin(35)sin(x) = 0
4. Simplify the equation further.
[(6 + 3cos(35)) - 7]cos(x) - 3sin(35)sin(x) = 0
(6 + 3cos(35) - 7)cos(x) - 3sin(35)sin(x) = 0
(3cos(35) - 1)cos(x) - 3sin(35)sin(x) = 0
5. Rearrange the terms to group them by trigonometric functions.
cos(x)(3cos(35) - 1) - sin(x)(3sin(35)) = 0
6. Apply the identity sin(A) = cos(90 - A) to replace sin(35) with cos(90 - 35).
cos(x)(3cos(35) - 1) - sin(x)(3cos(55)) = 0
7. Simplify further.
3cos(x)cos(35) - cos(x) - 3cos(55)sin(x) = 0
Now, we have simplified the equation and isolated the trigonometric functions on one side. Solving this equation might involve using other trigonometric identities or techniques specific to the problem at hand.