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受欢迎的三角函数 >

solvefor y,a*z=5sin(2y)

解答

求解

y, a \cdot z = 5 sin (2 y)

解答

y = \frac{arcsin ( \frac{a z}{5} )}{2} + πn, y = \frac{π}{2} + \frac{arcsin ( - \frac{a z}{5} )}{2} + πn

求解步骤

a z = 5 sin (2 y)

交换两边

5 sin (2 y) = a z

两边除以

5

5 sin (2 y) = a z

两边除以

5

\frac{5 sin ( 2 y )}{5} = \frac{a z}{5}

化简

sin (2 y) = \frac{a z}{5}

sin (2 y) = \frac{a z}{5}

使用反三角函数性质

sin (2 y) = \frac{a z}{5}

sin (2 y) = \frac{a z}{5}

的通解

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

2 y = arcsin (\frac{a z}{5}) + 2 πn, 2 y = π + arcsin (- \frac{a z}{5}) + 2 πn

2 y = arcsin (\frac{a z}{5}) + 2 πn, 2 y = π + arcsin (- \frac{a z}{5}) + 2 πn

解

2 y = arcsin (\frac{a z}{5}) + 2 πn : y = \frac{arcsin ( \frac{a z}{5} )}{2} + πn

2 y = arcsin (\frac{a z}{5}) + 2 πn

两边除以

2

2 y = arcsin (\frac{a z}{5}) + 2 πn

两边除以

2

\frac{2 y}{2} = \frac{arcsin ( \frac{a z}{5} )}{2} + \frac{2 πn}{2}

化简

y = \frac{arcsin ( \frac{a z}{5} )}{2} + πn

y = \frac{arcsin ( \frac{a z}{5} )}{2} + πn

解

2 y = π + arcsin (- \frac{a z}{5}) + 2 πn : y = \frac{π}{2} + \frac{arcsin ( - \frac{a z}{5} )}{2} + πn

2 y = π + arcsin (- \frac{a z}{5}) + 2 πn

两边除以

2

2 y = π + arcsin (- \frac{a z}{5}) + 2 πn

两边除以

2

\frac{2 y}{2} = \frac{π}{2} + \frac{arcsin ( - \frac{a z}{5} )}{2} + \frac{2 πn}{2}

化简

y = \frac{π}{2} + \frac{arcsin ( - \frac{a z}{5} )}{2} + πn

y = \frac{π}{2} + \frac{arcsin ( - \frac{a z}{5} )}{2} + πn

y = \frac{arcsin ( \frac{a z}{5} )}{2} + πn, y = \frac{π}{2} + \frac{arcsin ( - \frac{a z}{5} )}{2} + πn

作图

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