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受欢迎的三角函数 >

8sin(8x)+9=3

解答

8 sin (8 x) + 9 = 3

解答

x = - \frac{0.84806 \dots}{8} + \frac{πn}{4}, x = \frac{π}{8} + \frac{0.84806 \dots}{8} + \frac{πn}{4}

+1

度数

x = - 6.07379 \dots^{\circ} + 4 5^{\circ} n, x = 28.57379 \dots^{\circ} + 4 5^{\circ} n

求解步骤

8 sin (8 x) + 9 = 3

将

9

到右边

8 sin (8 x) + 9 = 3

两边减去

9

8 sin (8 x) + 9 - 9 = 3 - 9

化简

8 sin (8 x) = - 6

8 sin (8 x) = - 6

两边除以

8

8 sin (8 x) = - 6

两边除以

8

\frac{8 sin ( 8 x )}{8} = \frac{- 6}{8}

化简

\frac{8 sin ( 8 x )}{8} = \frac{- 6}{8}

化简

\frac{8 sin ( 8 x )}{8} : sin (8 x)

\frac{8 sin ( 8 x )}{8}

数字相除:

\frac{8}{8} = 1

= sin (8 x)

化简

\frac{- 6}{8} : - \frac{3}{4}

\frac{- 6}{8}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{6}{8}

约分:

2

= - \frac{3}{4}

sin (8 x) = - \frac{3}{4}

sin (8 x) = - \frac{3}{4}

sin (8 x) = - \frac{3}{4}

使用反三角函数性质

sin (8 x) = - \frac{3}{4}

sin (8 x) = - \frac{3}{4}

的通解

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

8 x = arcsin (- \frac{3}{4}) + 2 πn, 8 x = π + arcsin (\frac{3}{4}) + 2 πn

8 x = arcsin (- \frac{3}{4}) + 2 πn, 8 x = π + arcsin (\frac{3}{4}) + 2 πn

解

8 x = arcsin (- \frac{3}{4}) + 2 πn : x = - \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

8 x = arcsin (- \frac{3}{4}) + 2 πn

化简

arcsin (- \frac{3}{4}) + 2 πn : - arcsin (\frac{3}{4}) + 2 πn

arcsin (- \frac{3}{4}) + 2 πn

利用以下特性:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{3}{4}) = - arcsin (\frac{3}{4})

= - arcsin (\frac{3}{4}) + 2 πn

8 x = - arcsin (\frac{3}{4}) + 2 πn

两边除以

8

8 x = - arcsin (\frac{3}{4}) + 2 πn

两边除以

8

\frac{8 x}{8} = - \frac{arcsin ( \frac{3}{4} )}{8} + \frac{2 πn}{8}

化简

x = - \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

x = - \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

解

8 x = π + arcsin (\frac{3}{4}) + 2 πn : x = \frac{π}{8} + \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

8 x = π + arcsin (\frac{3}{4}) + 2 πn

两边除以

8

8 x = π + arcsin (\frac{3}{4}) + 2 πn

两边除以

8

\frac{8 x}{8} = \frac{π}{8} + \frac{arcsin ( \frac{3}{4} )}{8} + \frac{2 πn}{8}

化简

x = \frac{π}{8} + \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

x = \frac{π}{8} + \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

x = - \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}, x = \frac{π}{8} + \frac{arcsin ( \frac{3}{4} )}{8} + \frac{πn}{4}

以小数形式表示解

x = - \frac{0.84806 \dots}{8} + \frac{πn}{4}, x = \frac{π}{8} + \frac{0.84806 \dots}{8} + \frac{πn}{4}

作图

流行的例子

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