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受欢迎的三角函数 >

4sin(3x)-1=0

解答

4 sin (3 x) - 1 = 0

解答

x = \frac{0.25268 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{0.25268 \dots}{3} + \frac{2 πn}{3}

+1

度数

x = 4.82583 \dots^{\circ} + 12 0^{\circ} n, x = 55.17416 \dots^{\circ} + 12 0^{\circ} n

求解步骤

4 sin (3 x) - 1 = 0

将

1

到右边

4 sin (3 x) - 1 = 0

两边加上

1

4 sin (3 x) - 1 + 1 = 0 + 1

化简

4 sin (3 x) = 1

4 sin (3 x) = 1

两边除以

4

4 sin (3 x) = 1

两边除以

4

\frac{4 sin ( 3 x )}{4} = \frac{1}{4}

化简

sin (3 x) = \frac{1}{4}

sin (3 x) = \frac{1}{4}

使用反三角函数性质

sin (3 x) = \frac{1}{4}

sin (3 x) = \frac{1}{4}

的通解

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

3 x = arcsin (\frac{1}{4}) + 2 πn, 3 x = π - arcsin (\frac{1}{4}) + 2 πn

3 x = arcsin (\frac{1}{4}) + 2 πn, 3 x = π - arcsin (\frac{1}{4}) + 2 πn

解

3 x = arcsin (\frac{1}{4}) + 2 πn : x = \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

3 x = arcsin (\frac{1}{4}) + 2 πn

两边除以

3

3 x = arcsin (\frac{1}{4}) + 2 πn

两边除以

3

\frac{3 x}{3} = \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

化简

x = \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

x = \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

解

3 x = π - arcsin (\frac{1}{4}) + 2 πn : x = \frac{π}{3} - \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

3 x = π - arcsin (\frac{1}{4}) + 2 πn

两边除以

3

3 x = π - arcsin (\frac{1}{4}) + 2 πn

两边除以

3

\frac{3 x}{3} = \frac{π}{3} - \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

化简

x = \frac{π}{3} - \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

x = \frac{π}{3} - \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

x = \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{arcsin ( \frac{1}{4} )}{3} + \frac{2 πn}{3}

以小数形式表示解

x = \frac{0.25268 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{0.25268 \dots}{3} + \frac{2 πn}{3}

作图

流行的例子

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3 tan (2 x - π) + 1 = 0

7/4 cos(3θ)-1=0

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cos(x)=sin((7pi)/6),0<= x<= 2pi

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1.5=2.75cos(30(x-4))+3.25

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