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受欢迎的三角函数 >

6sin(3x)=5

解答

6 sin (3 x) = 5

解答

x = \frac{0.98511 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{0.98511 \dots}{3} + \frac{2 πn}{3}

+1

度数

x = 18.81423 \dots^{\circ} + 12 0^{\circ} n, x = 41.18576 \dots^{\circ} + 12 0^{\circ} n

求解步骤

6 sin (3 x) = 5

两边除以

6

6 sin (3 x) = 5

两边除以

6

\frac{6 sin ( 3 x )}{6} = \frac{5}{6}

化简

sin (3 x) = \frac{5}{6}

sin (3 x) = \frac{5}{6}

使用反三角函数性质

sin (3 x) = \frac{5}{6}

sin (3 x) = \frac{5}{6}

的通解

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

3 x = arcsin (\frac{5}{6}) + 2 πn, 3 x = π - arcsin (\frac{5}{6}) + 2 πn

3 x = arcsin (\frac{5}{6}) + 2 πn, 3 x = π - arcsin (\frac{5}{6}) + 2 πn

解

3 x = arcsin (\frac{5}{6}) + 2 πn : x = \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}

3 x = arcsin (\frac{5}{6}) + 2 πn

两边除以

3

3 x = arcsin (\frac{5}{6}) + 2 πn

两边除以

3

\frac{3 x}{3} = \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}

化简

x = \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}

x = \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}

解

3 x = π - arcsin (\frac{5}{6}) + 2 πn : x = \frac{π}{3} - \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}

3 x = π - arcsin (\frac{5}{6}) + 2 πn

两边除以

3

3 x = π - arcsin (\frac{5}{6}) + 2 πn

两边除以

3

\frac{3 x}{3} = \frac{π}{3} - \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}

化简

x = \frac{π}{3} - \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}

x = \frac{π}{3} - \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}

x = \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{arcsin ( \frac{5}{6} )}{3} + \frac{2 πn}{3}

以小数形式表示解

x = \frac{0.98511 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{0.98511 \dots}{3} + \frac{2 πn}{3}

作图

流行的例子

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