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 >

11cos(x)+6=-cos(x)

解答

11 cos (x) + 6 = - cos (x)

解答

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

+1

度数

x = 12 0^{\circ} + 36 0^{\circ} n, x = 24 0^{\circ} + 36 0^{\circ} n

求解步骤

11 cos (x) + 6 = - cos (x)

用替代法求解

11 cos (x) + 6 = - cos (x)

令

: cos (x) = u

11 u + 6 = - u

11 u + 6 = - u : u = - \frac{1}{2}

11 u + 6 = - u

将

6

到右边

11 u + 6 = - u

两边减去

6

11 u + 6 - 6 = - u - 6

化简

11 u = - u - 6

11 u = - u - 6

将

u

para o lado esquerdo

11 u = - u - 6

两边加上

u

11 u + u = - u - 6 + u

化简

12 u = - 6

12 u = - 6

两边除以

12

12 u = - 6

两边除以

12

\frac{12 u}{12} = \frac{- 6}{12}

化简

\frac{12 u}{12} = \frac{- 6}{12}

化简

\frac{12 u}{12} : u

\frac{12 u}{12}

数字相除:

\frac{12}{12} = 1

= u

化简

\frac{- 6}{12} : - \frac{1}{2}

\frac{- 6}{12}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{6}{12}

约分:

6

= - \frac{1}{2}

u = - \frac{1}{2}

u = - \frac{1}{2}

u = - \frac{1}{2}

u = cos (x)

代回

cos (x) = - \frac{1}{2}

cos (x) = - \frac{1}{2}

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

cos (x) = - \frac{1}{2}

cos (x) = - \frac{1}{2}

的通解

cos (x)

周期表（周期为

2 πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

合并所有解

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

作图

流行的例子

cos^2(x)=8sin^2(x)-6sin(x)

cos^{2} (x) = 8 sin^{2} (x) - 6 sin (x)

sqrt(3)sin(x)-cos(x)=1

3 sin (x) - cos (x) = 1

cos(x)sin(x)=-2sin(x)

cos (x) sin (x) = - 2 sin (x)

(csc(θ)-2)(cot(θ)+1)=0

(csc (θ) - 2) (cot (θ) + 1) = 0

sin (x) = csc (x)