4 costheta +3sintheta=5,4sintheta-3costheta=WHAT
4 sin(90-theta) + 3 sintheta
= 5.4 sintheta -3 sin(90-theta)
7 sin(90-theta) = 2.4 sintheta
7costheta = 2.4sintheta
tantheta = 2.917
theta = 71.08 degrees
Proceed to calculate either side of the original equation.
To find the value of the expression 4sinθ - 3cosθ, we can solve the given system of equations:
Equation 1: 4cosθ + 3sinθ = 5
Equation 2: 4sinθ - 3cosθ = ?
Here is how we can find the value:
Step 1: Rearrange Equation 1 to solve for sinθ:
4cosθ + 3sinθ = 5
3sinθ = 5 - 4cosθ
sinθ = (5 - 4cosθ) / 3
Step 2: Substitute the expression for sinθ into Equation 2:
4sinθ - 3cosθ = ?
4((5 - 4cosθ) / 3) - 3cosθ = ?
(20 - 16cosθ) / 3 - 3cosθ = ?
Step 3: Multiply both sides of the equation by 3 to eliminate the fraction:
3 * ((20 - 16cosθ) / 3) - 3 * 3cosθ = ?
20 - 16cosθ - 9cosθ = ?
Step 4: Combine like terms:
20 - 25cosθ = ?
Therefore, the value of 4sinθ - 3cosθ is given by the expression 20 - 25cosθ.
To find the value of the expression 4sin(theta) - 3cos(theta), we can solve the system of equations given by:
4cos(theta) + 3sin(theta) = 5 (Equation 1)
4sin(theta) - 3cos(theta) = WHAT (Equation 2)
First, let's rearrange Equation 2 to solve for WHAT:
4sin(theta) - 3cos(theta) = WHAT
=> WHAT = 4sin(theta) - 3cos(theta)
Now, we need to eliminate theta from the equations. To do this, we can square both equations:
(Equation 1)^2: (4cos(theta) + 3sin(theta))^2 = 5^2
=> 16cos^2(theta) + 24cos(theta)sin(theta) + 9sin^2(theta) = 25 (Equation 3)
(Equation 2)^2: (4sin(theta) - 3cos(theta))^2 = (WHAT)^2
=> 16sin^2(theta) - 24cos(theta)sin(theta) + 9cos^2(theta) = (WHAT)^2 (Equation 4)
Now, subtract Equation 4 from Equation 3:
16cos^2(theta) + 24cos(theta)sin(theta) + 9sin^2(theta) - (16sin^2(theta) - 24cos(theta)sin(theta) + 9cos^2(theta)) = 25 - (WHAT)^2
Simplifying and canceling out terms:
25cos^2(theta) + 25sin^2(theta) = 25 - (WHAT)^2
25(cos^2(theta) + sin^2(theta)) = 25 - (WHAT)^2
25(1) = 25 - (WHAT)^2
25 = 25 - (WHAT)^2
(WHAT)^2 = 0
WHAT = √0 = 0
Therefore, 4sin(theta) - 3cos(theta) = 0.