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受欢迎的三角函数 >

sin(2x)=-4/5

解答

sin (2 x) = - \frac{4}{5}

解答

x = - \frac{0.92729 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.92729 \dots}{2} + πn

+1

度数

x = - 26.56505 \dots^{\circ} + 18 0^{\circ} n, x = 116.56505 \dots^{\circ} + 18 0^{\circ} n

求解步骤

sin (2 x) = - \frac{4}{5}

使用反三角函数性质

sin (2 x) = - \frac{4}{5}

sin (2 x) = - \frac{4}{5}

的通解

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

2 x = arcsin (- \frac{4}{5}) + 2 πn, 2 x = π + arcsin (\frac{4}{5}) + 2 πn

2 x = arcsin (- \frac{4}{5}) + 2 πn, 2 x = π + arcsin (\frac{4}{5}) + 2 πn

解

2 x = arcsin (- \frac{4}{5}) + 2 πn : x = - \frac{arcsin ( \frac{4}{5} )}{2} + πn

2 x = arcsin (- \frac{4}{5}) + 2 πn

化简

arcsin (- \frac{4}{5}) + 2 πn : - arcsin (\frac{4}{5}) + 2 πn

arcsin (- \frac{4}{5}) + 2 πn

利用以下特性:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{4}{5}) = - arcsin (\frac{4}{5})

= - arcsin (\frac{4}{5}) + 2 πn

2 x = - arcsin (\frac{4}{5}) + 2 πn

两边除以

2

2 x = - arcsin (\frac{4}{5}) + 2 πn

两边除以

2

\frac{2 x}{2} = - \frac{arcsin ( \frac{4}{5} )}{2} + \frac{2 πn}{2}

化简

x = - \frac{arcsin ( \frac{4}{5} )}{2} + πn

x = - \frac{arcsin ( \frac{4}{5} )}{2} + πn

解

2 x = π + arcsin (\frac{4}{5}) + 2 πn : x = \frac{π}{2} + \frac{arcsin ( \frac{4}{5} )}{2} + πn

2 x = π + arcsin (\frac{4}{5}) + 2 πn

两边除以

2

2 x = π + arcsin (\frac{4}{5}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{π}{2} + \frac{arcsin ( \frac{4}{5} )}{2} + \frac{2 πn}{2}

化简

x = \frac{π}{2} + \frac{arcsin ( \frac{4}{5} )}{2} + πn

x = \frac{π}{2} + \frac{arcsin ( \frac{4}{5} )}{2} + πn

x = - \frac{arcsin ( \frac{4}{5} )}{2} + πn, x = \frac{π}{2} + \frac{arcsin ( \frac{4}{5} )}{2} + πn

以小数形式表示解

x = - \frac{0.92729 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.92729 \dots}{2} + πn

作图

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