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 >

3+3sin(θ)=3-3sin(θ)

解答

3 + 3 sin (θ) = 3 - 3 sin (θ)

解答

θ = 2 πn, θ = π + 2 πn

+1

度数

θ = 0^{\circ} + 36 0^{\circ} n, θ = 18 0^{\circ} + 36 0^{\circ} n

求解步骤

3 + 3 sin (θ) = 3 - 3 sin (θ)

用替代法求解

3 + 3 sin (θ) = 3 - 3 sin (θ)

令

: sin (θ) = u

3 + 3 u = 3 - 3 u

3 + 3 u = 3 - 3 u : u = 0

3 + 3 u = 3 - 3 u

两边减去

3

3 + 3 u - 3 = 3 - 3 u - 3

化简

3 u = - 3 u

将

3 u

para o lado esquerdo

3 u = - 3 u

两边加上

3 u

3 u + 3 u = - 3 u + 3 u

化简

6 u = 0

6 u = 0

两边除以

6

6 u = 0

两边除以

6

\frac{6 u}{6} = \frac{0}{6}

化简

u = 0

u = 0

u = sin (θ)

代回

sin (θ) = 0

sin (θ) = 0

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

sin (θ) = 0

sin (θ) = 0

的通解

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

θ = 0 + 2 πn, θ = π + 2 πn

θ = 0 + 2 πn, θ = π + 2 πn

解

θ = 0 + 2 πn : θ = 2 πn

θ = 0 + 2 πn

0 + 2 πn = 2 πn

θ = 2 πn

θ = 2 πn, θ = π + 2 πn

合并所有解

θ = 2 πn, θ = π + 2 πn

作图

流行的例子

(sin(C))/(18)=(sin(63))/(17)

\frac{sin ( C )}{18} = \frac{sin ( 6 3 ^{\circ} )}{17}

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

(-(3*cos(Q^1)))/2 =0

\frac{- ( 3 \cdot cos ( Q ^{1} ) )}{2} = 0

tan^2(x)+sqrt(3)tan(x)=0,0<= x<360

tan^{2} (x) + 3 tan (x) = 0, 0^{\circ} \leq x < 36 0^{\circ}

1/2 (6.50941)+cos(θ)(10.40478)=12

\frac{1}{2} (6.50941) + cos (θ) (10.40478) = 12