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受欢迎的三角函数 >

11sin(B)-1=3sin(B)-1

解答

11 sin (B) - 1 = 3 sin (B) - 1

解答

B = 2 πn, B = π + 2 πn

+1

度数

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

求解步骤

11 sin (B) - 1 = 3 sin (B) - 1

用替代法求解

11 sin (B) - 1 = 3 sin (B) - 1

令

: sin (B) = u

11 u - 1 = 3 u - 1

11 u - 1 = 3 u - 1 : u = 0

11 u - 1 = 3 u - 1

两边加上

1

11 u - 1 + 1 = 3 u - 1 + 1

化简

11 u = 3 u

将

3 u

para o lado esquerdo

11 u = 3 u

两边减去

3 u

11 u - 3 u = 3 u - 3 u

化简

8 u = 0

8 u = 0

两边除以

8

8 u = 0

两边除以

8

\frac{8 u}{8} = \frac{0}{8}

化简

u = 0

u = 0

u = sin (B)

代回

sin (B) = 0

sin (B) = 0

sin (B) = 0 : B = 2 πn, B = π + 2 πn

sin (B) = 0

sin (B) = 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}

B = 0 + 2 πn, B = π + 2 πn

B = 0 + 2 πn, B = π + 2 πn

解

B = 0 + 2 πn : B = 2 πn

B = 0 + 2 πn

0 + 2 πn = 2 πn

B = 2 πn

B = 2 πn, B = π + 2 πn

合并所有解

B = 2 πn, B = π + 2 πn

作图

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