What is the general solution for solvefor v,a=arctan((v^2)/(gR)) ?

The general solution for solvefor v,a=arctan((v^2)/(gR)) is v=sqrt(tan(a)gR),v=-sqrt(tan(a)gR)

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solvefor v,a=arctan((v^2)/(gR))

solve for

v, a = arctan (\frac{v ^{2}}{g R})

v = tan (a) g R, v = - tan (a) g R

Solution steps

a = arctan (\frac{v ^{2}}{g R})

Switch sides

arctan (\frac{v ^{2}}{g R}) = a

Apply trig inverse properties

arctan (\frac{v ^{2}}{g R}) = a

arctan (x) = a \Rightarrow x = tan (a)

\frac{v ^{2}}{g R} = tan (a)

\frac{v ^{2}}{g R} = tan (a)

Solve

\frac{v ^{2}}{g R} = tan (a) : v = tan (a) g R, v = - tan (a) g R; g R \neq = 0

\frac{v ^{2}}{g R} = tan (a)

Multiply both sides by

g R

\frac{v ^{2}}{g R} = tan (a)

Multiply both sides by

g R

\frac{v ^{2} g R}{g R} = tan (a) g R; g R \neq = 0

Simplify

v^{2} = tan (a) g R; g R \neq = 0

v^{2} = tan (a) g R; g R \neq = 0

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

v = tan (a) g R, v = - tan (a) g R; g R \neq = 0

v = tan (a) g R, v = - tan (a) g R

3 sin^{2} (x) = 4 sin (x)

5 sin (θ) = 4

2 cos^{2} (x) - 7 cos (x) = 0

2 cos^{2} (x) - 7 cos (x) = 3

tan (x) = tan (2 x)

What is the general solution for solvefor v,a=arctan((v^2)/(gR)) ?
The general solution for solvefor v,a=arctan((v^2)/(gR)) is v=sqrt(tan(a)gR),v=-sqrt(tan(a)gR)