What is the general solution for solvefor θ,W=F*d*cos(θ) ?

The general solution for solvefor θ,W=F*d*cos(θ) is θ=arccos(W/(Fd))+2pin,θ=-arccos(W/(Fd))+2pin

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solvefor θ,W=Fdcos(θ)

solve for

θ, W = F \cdot d \cdot cos (θ)

θ = arccos (\frac{W}{F d}) + 2 πn, θ = - arccos (\frac{W}{F d}) + 2 πn

Solution steps

W = F d cos (θ)

Switch sides

F d cos (θ) = W

Divide both sides by

F d; F d \neq = 0

F d cos (θ) = W

Divide both sides by

F d; F d \neq = 0

\frac{F d cos ( θ )}{F d} = \frac{W}{F d}; F d \neq = 0

Simplify

cos (θ) = \frac{W}{F d}; F d \neq = 0

cos (θ) = \frac{W}{F d}; F d \neq = 0

Apply trig inverse properties

cos (θ) = \frac{W}{F d}

General solutions for

cos (θ) = \frac{W}{F d}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

θ = arccos (\frac{W}{F d}) + 2 πn, θ = - arccos (\frac{W}{F d}) + 2 πn

θ = arccos (\frac{W}{F d}) + 2 πn, θ = - arccos (\frac{W}{F d}) + 2 πn

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\frac{1}{4} sin (8 x) = - \frac{1}{8}, 2 cos (8 x) = 3

sin (x) - sin (2 x) = 0, 0 \leq x < 2 π

What is the general solution for solvefor θ,W=F*d*cos(θ) ?
The general solution for solvefor θ,W=F*d*cos(θ) is θ=arccos(W/(Fd))+2pin,θ=-arccos(W/(Fd))+2pin