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受欢迎的三角函数 >

0.3=sin(9x)

解答

0.3 = sin (9 x)

解答

x = \frac{0.30469 \dots}{9} + \frac{2 πn}{9}, x = \frac{π}{9} - \frac{0.30469 \dots}{9} + \frac{2 πn}{9}

+1

度数

x = 1.93973 \dots^{\circ} + 4 0^{\circ} n, x = 18.06026 \dots^{\circ} + 4 0^{\circ} n

求解步骤

0.3 = sin (9 x)

交换两边

sin (9 x) = 0.3

使用反三角函数性质

sin (9 x) = 0.3

sin (9 x) = 0.3

的通解

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

9 x = arcsin (0.3) + 2 πn, 9 x = π - arcsin (0.3) + 2 πn

9 x = arcsin (0.3) + 2 πn, 9 x = π - arcsin (0.3) + 2 πn

解

9 x = arcsin (0.3) + 2 πn : x = \frac{arcsin ( 0.3 )}{9} + \frac{2 πn}{9}

9 x = arcsin (0.3) + 2 πn

两边除以

9

9 x = arcsin (0.3) + 2 πn

两边除以

9

\frac{9 x}{9} = \frac{arcsin ( 0.3 )}{9} + \frac{2 πn}{9}

化简

x = \frac{arcsin ( 0.3 )}{9} + \frac{2 πn}{9}

x = \frac{arcsin ( 0.3 )}{9} + \frac{2 πn}{9}

解

9 x = π - arcsin (0.3) + 2 πn : x = \frac{π}{9} - \frac{arcsin ( 0.3 )}{9} + \frac{2 πn}{9}

9 x = π - arcsin (0.3) + 2 πn

两边除以

9

9 x = π - arcsin (0.3) + 2 πn

两边除以

9

\frac{9 x}{9} = \frac{π}{9} - \frac{arcsin ( 0.3 )}{9} + \frac{2 πn}{9}

化简

x = \frac{π}{9} - \frac{arcsin ( 0.3 )}{9} + \frac{2 πn}{9}

x = \frac{π}{9} - \frac{arcsin ( 0.3 )}{9} + \frac{2 πn}{9}

x = \frac{arcsin ( 0.3 )}{9} + \frac{2 πn}{9}, x = \frac{π}{9} - \frac{arcsin ( 0.3 )}{9} + \frac{2 πn}{9}

以小数形式表示解

x = \frac{0.30469 \dots}{9} + \frac{2 πn}{9}, x = \frac{π}{9} - \frac{0.30469 \dots}{9} + \frac{2 πn}{9}

作图

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