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 >

1+sin(θ)=2-sin(θ)

解答

1 + sin (θ) = 2 - sin (θ)

解答

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

+1

度数

θ = 3 0^{\circ} + 36 0^{\circ} n, θ = 15 0^{\circ} + 36 0^{\circ} n

求解步骤

1 + sin (θ) = 2 - sin (θ)

用替代法求解

1 + sin (θ) = 2 - sin (θ)

令

: sin (θ) = u

1 + u = 2 - u

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

1 + u = 2 - u

将

1

到右边

1 + u = 2 - u

两边减去

1

1 + u - 1 = 2 - u - 1

化简

u = - u + 1

u = - u + 1

将

u

para o lado esquerdo

u = - u + 1

两边加上

u

u + u = - u + 1 + u

化简

2 u = 1

2 u = 1

两边除以

2

2 u = 1

两边除以

2

\frac{2 u}{2} = \frac{1}{2}

化简

u = \frac{1}{2}

u = \frac{1}{2}

u = sin (θ)

代回

sin (θ) = \frac{1}{2}

sin (θ) = \frac{1}{2}

sin (θ) = \frac{1}{2} : θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

sin (θ) = \frac{1}{2}

sin (θ) = \frac{1}{2}

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 = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

合并所有解

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

作图

流行的例子

-4cos^2(θ)+cos(θ)=9cos(θ)+3

- 4 cos^{2} (θ) + cos (θ) = 9 cos (θ) + 3

3+4cot(x)=5csc(x)

3 + 4 cot (x) = 5 csc (x)

(tan(x)-1)(sec(x)+1)=0

(tan (x) - 1) (sec (x) + 1) = 0

tan (θ) = \frac{9}{10}

tan(x)= 3/(sqrt(205))

tan (x) = \frac{3}{205}