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受欢迎的三角函数 >

6sin(8x)+2=-3

解答

6 sin (8 x) + 2 = - 3

解答

x = - \frac{0.98511 \dots}{8} + \frac{πn}{4}, x = \frac{π}{8} + \frac{0.98511 \dots}{8} + \frac{πn}{4}

+1

度数

x = - 7.05533 \dots^{\circ} + 4 5^{\circ} n, x = 29.55533 \dots^{\circ} + 4 5^{\circ} n

求解步骤

6 sin (8 x) + 2 = - 3

将

2

到右边

6 sin (8 x) + 2 = - 3

两边减去

2

6 sin (8 x) + 2 - 2 = - 3 - 2

化简

6 sin (8 x) = - 5

6 sin (8 x) = - 5

两边除以

6

6 sin (8 x) = - 5

两边除以

6

\frac{6 sin ( 8 x )}{6} = \frac{- 5}{6}

化简

sin (8 x) = - \frac{5}{6}

sin (8 x) = - \frac{5}{6}

使用反三角函数性质

sin (8 x) = - \frac{5}{6}

sin (8 x) = - \frac{5}{6}

的通解

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

8 x = arcsin (- \frac{5}{6}) + 2 πn, 8 x = π + arcsin (\frac{5}{6}) + 2 πn

8 x = arcsin (- \frac{5}{6}) + 2 πn, 8 x = π + arcsin (\frac{5}{6}) + 2 πn

解

8 x = arcsin (- \frac{5}{6}) + 2 πn : x = - \frac{arcsin ( \frac{5}{6} )}{8} + \frac{πn}{4}

8 x = arcsin (- \frac{5}{6}) + 2 πn

化简

arcsin (- \frac{5}{6}) + 2 πn : - arcsin (\frac{5}{6}) + 2 πn

arcsin (- \frac{5}{6}) + 2 πn

利用以下特性:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{5}{6}) = - arcsin (\frac{5}{6})

= - arcsin (\frac{5}{6}) + 2 πn

8 x = - arcsin (\frac{5}{6}) + 2 πn

两边除以

8

8 x = - arcsin (\frac{5}{6}) + 2 πn

两边除以

8

\frac{8 x}{8} = - \frac{arcsin ( \frac{5}{6} )}{8} + \frac{2 πn}{8}

化简

x = - \frac{arcsin ( \frac{5}{6} )}{8} + \frac{πn}{4}

x = - \frac{arcsin ( \frac{5}{6} )}{8} + \frac{πn}{4}

解

8 x = π + arcsin (\frac{5}{6}) + 2 πn : x = \frac{π}{8} + \frac{arcsin ( \frac{5}{6} )}{8} + \frac{πn}{4}

8 x = π + arcsin (\frac{5}{6}) + 2 πn

两边除以

8

8 x = π + arcsin (\frac{5}{6}) + 2 πn

两边除以

8

\frac{8 x}{8} = \frac{π}{8} + \frac{arcsin ( \frac{5}{6} )}{8} + \frac{2 πn}{8}

化简

x = \frac{π}{8} + \frac{arcsin ( \frac{5}{6} )}{8} + \frac{πn}{4}

x = \frac{π}{8} + \frac{arcsin ( \frac{5}{6} )}{8} + \frac{πn}{4}

x = - \frac{arcsin ( \frac{5}{6} )}{8} + \frac{πn}{4}, x = \frac{π}{8} + \frac{arcsin ( \frac{5}{6} )}{8} + \frac{πn}{4}

以小数形式表示解

x = - \frac{0.98511 \dots}{8} + \frac{πn}{4}, x = \frac{π}{8} + \frac{0.98511 \dots}{8} + \frac{πn}{4}

作图

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