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 >

6cos(θ)=-6(1+cos(θ))

解答

6 cos (θ) = - 6 (1 + cos (θ))

解答

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

+1

度数

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

求解步骤

6 cos (θ) = - 6 (1 + cos (θ))

用替代法求解

6 cos (θ) = - 6 (1 + cos (θ))

令

: cos (θ) = u

6 u = - 6 (1 + u)

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

6 u = - 6 (1 + u)

展开

- 6 (1 + u) : - 6 - 6 u

- 6 (1 + u)

使用分配律:

a (b + c) = ab + a c

a = - 6, b = 1, c = u

= - 6 \cdot 1 + (- 6) u

使用加减运算法则

+ (- a) = - a

= - 6 \cdot 1 - 6 u

数字相乘:

6 \cdot 1 = 6

= - 6 - 6 u

6 u = - 6 - 6 u

将

6 u

para o lado esquerdo

6 u = - 6 - 6 u

两边加上

6 u

6 u + 6 u = - 6 - 6 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 (θ)

代回

cos (θ) = - \frac{1}{2}

cos (θ) = - \frac{1}{2}

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

cos (θ) = - \frac{1}{2}

cos (θ) = - \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}

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

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

合并所有解

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

作图

流行的例子

2sin^2(x)+5sin(x)+3=0

2 sin^{2} (x) + 5 sin (x) + 3 = 0

cos (A) = \frac{4}{5}

arcsin(x-2)= pi/6

arcsin (x - 2) = \frac{π}{6}

9.8sin(x)-1.96cos(x)=8.54

9.8 sin (x) - 1.96 cos (x) = 8.54

3/(cot(x))=8-5tan(x)

\frac{3}{cot ( x )} = 8 - 5 tan (x)