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受欢迎的三角函数 >

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

解答

求解

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

解答

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

求解步骤

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

交换两边

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

在两边乘以

g

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

在两边乘以

g

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

化简

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

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

两边除以

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

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

两边除以

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

化简

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

使用反三角函数性质

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

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

的通解

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

解

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

两边除以

2

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

两边除以

2

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

化简

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

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

解

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

两边除以

2

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

两边除以

2

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

化简

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

作图

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