What is the general solution for r=2acos(x) ?

The general solution for r=2acos(x) is x=arccos(r/(2a))+2pin,x=-arccos(r/(2a))+2pin

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r=2acos(x)

r = 2 a cos (x)

x = arccos (\frac{r}{2 a}) + 2 πn, x = - arccos (\frac{r}{2 a}) + 2 πn

Solution steps

r = 2 a cos (x)

Switch sides

2 a cos (x) = r

Divide both sides by

2 a; a \neq = 0

2 a cos (x) = r

Divide both sides by

2 a; a \neq = 0

\frac{2 a cos ( x )}{2 a} = \frac{r}{2 a}; a \neq = 0

Simplify

cos (x) = \frac{r}{2 a}; a \neq = 0

cos (x) = \frac{r}{2 a}; a \neq = 0

Apply trig inverse properties

cos (x) = \frac{r}{2 a}

General solutions for

cos (x) = \frac{r}{2 a}

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

x = arccos (\frac{r}{2 a}) + 2 πn, x = - arccos (\frac{r}{2 a}) + 2 πn

x = arccos (\frac{r}{2 a}) + 2 πn, x = - arccos (\frac{r}{2 a}) + 2 πn

What is the general solution for r=2acos(x) ?
The general solution for r=2acos(x) is x=arccos(r/(2a))+2pin,x=-arccos(r/(2a))+2pin