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受欢迎的三角函数 >

3sin(B)-2=5sin(B)-1

解答

3 sin (B) - 2 = 5 sin (B) - 1

解答

B = \frac{7 π}{6} + 2 πn, B = \frac{11 π}{6} + 2 πn

+1

度数

B = 21 0^{\circ} + 36 0^{\circ} n, B = 33 0^{\circ} + 36 0^{\circ} n

求解步骤

3 sin (B) - 2 = 5 sin (B) - 1

用替代法求解

3 sin (B) - 2 = 5 sin (B) - 1

令

: sin (B) = u

3 u - 2 = 5 u - 1

3 u - 2 = 5 u - 1 : u = - \frac{1}{2}

3 u - 2 = 5 u - 1

将

2

到右边

3 u - 2 = 5 u - 1

两边加上

2

3 u - 2 + 2 = 5 u - 1 + 2

化简

3 u = 5 u + 1

3 u = 5 u + 1

将

5 u

para o lado esquerdo

3 u = 5 u + 1

两边减去

5 u

3 u - 5 u = 5 u + 1 - 5 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 (B)

代回

sin (B) = - \frac{1}{2}

sin (B) = - \frac{1}{2}

sin (B) = - \frac{1}{2} : B = \frac{7 π}{6} + 2 πn, B = \frac{11 π}{6} + 2 πn

sin (B) = - \frac{1}{2}

sin (B) = - \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}

B = \frac{7 π}{6} + 2 πn, B = \frac{11 π}{6} + 2 πn

B = \frac{7 π}{6} + 2 πn, B = \frac{11 π}{6} + 2 πn

合并所有解

B = \frac{7 π}{6} + 2 πn, B = \frac{11 π}{6} + 2 πn

作图

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