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受欢迎的三角函数 >

4cos(4x)=3

解答

4 cos (4 x) = 3

解答

x = \frac{0.72273 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{0.72273 \dots}{4} + \frac{πn}{2}

+1

度数

x = 10.35240 \dots^{\circ} + 9 0^{\circ} n, x = 79.64759 \dots^{\circ} + 9 0^{\circ} n

求解步骤

4 cos (4 x) = 3

两边除以

4

4 cos (4 x) = 3

两边除以

4

\frac{4 cos ( 4 x )}{4} = \frac{3}{4}

化简

cos (4 x) = \frac{3}{4}

cos (4 x) = \frac{3}{4}

使用反三角函数性质

cos (4 x) = \frac{3}{4}

cos (4 x) = \frac{3}{4}

的通解

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

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

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

解

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

4 x = arccos (\frac{3}{4}) + 2 πn

两边除以

4

4 x = arccos (\frac{3}{4}) + 2 πn

两边除以

4

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

化简

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

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

解

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

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

两边除以

4

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

两边除以

4

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

化简

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

化简

\frac{4 x}{4} : x

\frac{4 x}{4}

数字相除:

\frac{4}{4} = 1

= x

化简

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

\frac{2 π}{4} - \frac{arccos ( \frac{3}{4} )}{4} + \frac{2 πn}{4}

消掉

\frac{2 π}{4} : \frac{π}{2}

\frac{2 π}{4}

约分:

2

= \frac{π}{2}

= \frac{π}{2} - \frac{arccos ( \frac{3}{4} )}{4} + \frac{2 πn}{4}

消掉

\frac{2 πn}{4} : \frac{πn}{2}

\frac{2 πn}{4}

约分:

2

= \frac{πn}{2}

= \frac{π}{2} - \frac{arccos ( \frac{3}{4} )}{4} + \frac{πn}{2}

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

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

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

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

以小数形式表示解

x = \frac{0.72273 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{0.72273 \dots}{4} + \frac{πn}{2}

作图

流行的例子

sin(θ)=-2/(sqrt(2))

solvefor x,sin(x)= 2/3