What is the general solution for solvefor x,y=fcos(x) ?

The general solution for solvefor x,y=fcos(x) is x=arccos(y/f)+2pin,x=-arccos(y/f)+2pin

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solvefor x,y=fcos(x)

solve for

x, y = f cos (x)

x = arccos (\frac{y}{f}) + 2 πn, x = - arccos (\frac{y}{f}) + 2 πn

Solution steps

y = f cos (x)

Switch sides

f cos (x) = y

Divide both sides by

f; f \neq = 0

f cos (x) = y

Divide both sides by

f; f \neq = 0

\frac{f cos ( x )}{f} = \frac{y}{f}; f \neq = 0

Simplify

cos (x) = \frac{y}{f}; f \neq = 0

cos (x) = \frac{y}{f}; f \neq = 0

Apply trig inverse properties

cos (x) = \frac{y}{f}

General solutions for

cos (x) = \frac{y}{f}

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

x = arccos (\frac{y}{f}) + 2 πn, x = - arccos (\frac{y}{f}) + 2 πn

x = arccos (\frac{y}{f}) + 2 πn, x = - arccos (\frac{y}{f}) + 2 πn

3 cot (2 x) = - 1, 0 \leq x \leq π

5 sin^{2} (x) - cos (x) = 2

(cot (θ) - 1) (2 sin (θ) + 3) = 0

\frac{cos ( x ) - cos ^{2} ( x )}{sin ( x )} = sin (x) cos (x)

1 = - cot^{2} (x) + 2

What is the general solution for solvefor x,y=fcos(x) ?
The general solution for solvefor x,y=fcos(x) is x=arccos(y/f)+2pin,x=-arccos(y/f)+2pin