zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

7cos(4x)=6

解答

7 cos (4 x) = 6

解答

x = \frac{0.54109 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{0.54109 \dots}{4} + \frac{πn}{2}

+1

度数

x = 7.75067 \dots^{\circ} + 9 0^{\circ} n, x = 82.24932 \dots^{\circ} + 9 0^{\circ} n

求解步骤

7 cos (4 x) = 6

两边除以

7

7 cos (4 x) = 6

两边除以

7

\frac{7 cos ( 4 x )}{7} = \frac{6}{7}

化简

cos (4 x) = \frac{6}{7}

cos (4 x) = \frac{6}{7}

使用反三角函数性质

cos (4 x) = \frac{6}{7}

cos (4 x) = \frac{6}{7}

的通解

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

4 x = arccos (\frac{6}{7}) + 2 πn, 4 x = 2 π - arccos (\frac{6}{7}) + 2 πn

4 x = arccos (\frac{6}{7}) + 2 πn, 4 x = 2 π - arccos (\frac{6}{7}) + 2 πn

解

4 x = arccos (\frac{6}{7}) + 2 πn : x = \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}

4 x = arccos (\frac{6}{7}) + 2 πn

两边除以

4

4 x = arccos (\frac{6}{7}) + 2 πn

两边除以

4

\frac{4 x}{4} = \frac{arccos ( \frac{6}{7} )}{4} + \frac{2 πn}{4}

化简

x = \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}

x = \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}

解

4 x = 2 π - arccos (\frac{6}{7}) + 2 πn : x = \frac{π}{2} - \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}

4 x = 2 π - arccos (\frac{6}{7}) + 2 πn

两边除以

4

4 x = 2 π - arccos (\frac{6}{7}) + 2 πn

两边除以

4

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{6}{7} )}{4} + \frac{2 πn}{4}

化简

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{6}{7} )}{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{6}{7} )}{4} + \frac{2 πn}{4} : \frac{π}{2} - \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}

\frac{2 π}{4} - \frac{arccos ( \frac{6}{7} )}{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{6}{7} )}{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{6}{7} )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}

x = \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{arccos ( \frac{6}{7} )}{4} + \frac{πn}{2}

以小数形式表示解

x = \frac{0.54109 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{0.54109 \dots}{4} + \frac{πn}{2}

作图

流行的例子

-120=-90-arctan(0.1)+arctan(0.1x)

- 120 = - 90 - arctan (0.1) + arctan (0.1 x)

3 tan (x) = 0

2sin^2(x)-15sin(x)+7=0

2 sin^{2} (x) - 15 sin (x) + 7 = 0

solvefor x,cos(x)=(-3)/5

so l v e f or x, cos (x) = \frac{- 3}{5}

4sin^2(x)=4cos(x)+5

4 sin^{2} (x) = 4 cos (x) + 5