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受欢迎的三角函数 >

6sin(4x)+4=5

解答

6 sin (4 x) + 4 = 5

解答

x = \frac{0.16744 \dots}{4} + \frac{πn}{2}, x = \frac{π}{4} - \frac{0.16744 \dots}{4} + \frac{πn}{2}

+1

度数

x = 2.39851 \dots^{\circ} + 9 0^{\circ} n, x = 42.60148 \dots^{\circ} + 9 0^{\circ} n

求解步骤

6 sin (4 x) + 4 = 5

将

4

到右边

6 sin (4 x) + 4 = 5

两边减去

4

6 sin (4 x) + 4 - 4 = 5 - 4

化简

6 sin (4 x) = 1

6 sin (4 x) = 1

两边除以

6

6 sin (4 x) = 1

两边除以

6

\frac{6 sin ( 4 x )}{6} = \frac{1}{6}

化简

sin (4 x) = \frac{1}{6}

sin (4 x) = \frac{1}{6}

使用反三角函数性质

sin (4 x) = \frac{1}{6}

sin (4 x) = \frac{1}{6}

的通解

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

4 x = arcsin (\frac{1}{6}) + 2 πn, 4 x = π - arcsin (\frac{1}{6}) + 2 πn

4 x = arcsin (\frac{1}{6}) + 2 πn, 4 x = π - arcsin (\frac{1}{6}) + 2 πn

解

4 x = arcsin (\frac{1}{6}) + 2 πn : x = \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

4 x = arcsin (\frac{1}{6}) + 2 πn

两边除以

4

4 x = arcsin (\frac{1}{6}) + 2 πn

两边除以

4

\frac{4 x}{4} = \frac{arcsin ( \frac{1}{6} )}{4} + \frac{2 πn}{4}

化简

x = \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

x = \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

解

4 x = π - arcsin (\frac{1}{6}) + 2 πn : x = \frac{π}{4} - \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

4 x = π - arcsin (\frac{1}{6}) + 2 πn

两边除以

4

4 x = π - arcsin (\frac{1}{6}) + 2 πn

两边除以

4

\frac{4 x}{4} = \frac{π}{4} - \frac{arcsin ( \frac{1}{6} )}{4} + \frac{2 πn}{4}

化简

x = \frac{π}{4} - \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

x = \frac{π}{4} - \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

x = \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}, x = \frac{π}{4} - \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

以小数形式表示解

x = \frac{0.16744 \dots}{4} + \frac{πn}{2}, x = \frac{π}{4} - \frac{0.16744 \dots}{4} + \frac{πn}{2}

作图

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