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Popular >

solvefor x,R=(v^2sin(2x))/g

Solution

solve for

x, R = \frac{v ^{2} sin ( 2 x )}{g}

Solution

x = \frac{arcsin ( \frac{R g}{v ^{2}} )}{2} + πn, x = \frac{π}{2} + \frac{arcsin ( - \frac{R g}{v ^{2}} )}{2} + πn

Solution steps

R = \frac{v ^{2} sin ( 2 x )}{g}

Switch sides

\frac{v ^{2} sin ( 2 x )}{g} = R

Multiply both sides by

g

\frac{v ^{2} sin ( 2 x )}{g} = R

Multiply both sides by

g

\frac{v ^{2} sin ( 2 x ) g}{g} = R g; g \neq = 0

Simplify

v^{2} sin (2 x) = R g; g \neq = 0

v^{2} sin (2 x) = R g; g \neq = 0

Divide both sides by

v^{2}; g \neq = 0, v \neq = 0

v^{2} sin (2 x) = R g; g \neq = 0

Divide both sides by

v^{2}; g \neq = 0, v \neq = 0

\frac{v ^{2} sin ( 2 x )}{v ^{2}} = \frac{R g}{v ^{2}}; g \neq = 0, v \neq = 0

Simplify

sin (2 x) = \frac{R g}{v ^{2}}; g \neq = 0, v \neq = 0

sin (2 x) = \frac{R g}{v ^{2}}; g \neq = 0, v \neq = 0

Apply trig inverse properties

sin (2 x) = \frac{R g}{v ^{2}}

General solutions for

sin (2 x) = \frac{R g}{v ^{2}}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

2 x = arcsin (\frac{R g}{v ^{2}}) + 2 πn, 2 x = π + arcsin (- \frac{R g}{v ^{2}}) + 2 πn

2 x = arcsin (\frac{R g}{v ^{2}}) + 2 πn, 2 x = π + arcsin (- \frac{R g}{v ^{2}}) + 2 πn

Solve

2 x = arcsin (\frac{R g}{v ^{2}}) + 2 πn : x = \frac{arcsin ( \frac{R g}{v ^{2}} )}{2} + πn

2 x = arcsin (\frac{R g}{v ^{2}}) + 2 πn

Divide both sides by

2

2 x = arcsin (\frac{R g}{v ^{2}}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{arcsin ( \frac{R g}{v ^{2}} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{arcsin ( \frac{R g}{v ^{2}} )}{2} + πn

x = \frac{arcsin ( \frac{R g}{v ^{2}} )}{2} + πn

Solve

2 x = π + arcsin (- \frac{R g}{v ^{2}}) + 2 πn : x = \frac{π}{2} + \frac{arcsin ( - \frac{R g}{v ^{2}} )}{2} + πn

2 x = π + arcsin (- \frac{R g}{v ^{2}}) + 2 πn

Divide both sides by

2

2 x = π + arcsin (- \frac{R g}{v ^{2}}) + 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{π}{2} + \frac{arcsin ( - \frac{R g}{v ^{2}} )}{2} + \frac{2 πn}{2}

Simplify

x = \frac{π}{2} + \frac{arcsin ( - \frac{R g}{v ^{2}} )}{2} + πn

x = \frac{π}{2} + \frac{arcsin ( - \frac{R g}{v ^{2}} )}{2} + πn

x = \frac{arcsin ( \frac{R g}{v ^{2}} )}{2} + πn, x = \frac{π}{2} + \frac{arcsin ( - \frac{R g}{v ^{2}} )}{2} + πn

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