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受欢迎的三角函数 >

sin(x)+1=2sin(x)

解答

sin (x) + 1 = 2 sin (x)

解答

x = \frac{π}{2} + 2 πn

+1

度数

x = 9 0^{\circ} + 36 0^{\circ} n

求解步骤

sin (x) + 1 = 2 sin (x)

用替代法求解

sin (x) + 1 = 2 sin (x)

令

: sin (x) = u

u + 1 = 2 u

u + 1 = 2 u : u = 1

u + 1 = 2 u

将

1

到右边

u + 1 = 2 u

两边减去

1

u + 1 - 1 = 2 u - 1

化简

u = 2 u - 1

u = 2 u - 1

将

2 u

para o lado esquerdo

u = 2 u - 1

两边减去

2 u

u - 2 u = 2 u - 1 - 2 u

化简

- u = - 1

- u = - 1

两边除以

- 1

- u = - 1

两边除以

- 1

\frac{- u}{- 1} = \frac{- 1}{- 1}

化简

u = 1

u = 1

u = sin (x)

代回

sin (x) = 1

sin (x) = 1

sin (x) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = 1

sin (x) = 1

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}

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

合并所有解

x = \frac{π}{2} + 2 πn

作图

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