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受欢迎的三角函数 >

5sin(4x)=2

解答

5 sin (4 x) = 2

解答

x = \frac{0.41151 \dots}{4} + \frac{πn}{2}, x = \frac{π}{4} - \frac{0.41151 \dots}{4} + \frac{πn}{2}

+1

度数

x = 5.89454 \dots^{\circ} + 9 0^{\circ} n, x = 39.10545 \dots^{\circ} + 9 0^{\circ} n

求解步骤

5 sin (4 x) = 2

两边除以

5

5 sin (4 x) = 2

两边除以

5

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

化简

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

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

使用反三角函数性质

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

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

的通解

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

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

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

解

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

4 x = arcsin (\frac{2}{5}) + 2 πn

两边除以

4

4 x = arcsin (\frac{2}{5}) + 2 πn

两边除以

4

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

化简

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

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

解

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

4 x = π - arcsin (\frac{2}{5}) + 2 πn

两边除以

4

4 x = π - arcsin (\frac{2}{5}) + 2 πn

两边除以

4

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

化简

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

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

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

以小数形式表示解

x = \frac{0.41151 \dots}{4} + \frac{πn}{2}, x = \frac{π}{4} - \frac{0.41151 \dots}{4} + \frac{πn}{2}

作图

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