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受欢迎的三角函数 >

-sin(B)-4=3sin(B)-5

解答

- sin (B) - 4 = 3 sin (B) - 5

解答

B = 0.25268 \dots + 2 πn, B = π - 0.25268 \dots + 2 πn

+1

度数

B = 14.47751 \dots^{\circ} + 36 0^{\circ} n, B = 165.52248 \dots^{\circ} + 36 0^{\circ} n

求解步骤

- sin (B) - 4 = 3 sin (B) - 5

用替代法求解

- sin (B) - 4 = 3 sin (B) - 5

令

: sin (B) = u

- u - 4 = 3 u - 5

- u - 4 = 3 u - 5 : u = \frac{1}{4}

- u - 4 = 3 u - 5

将

4

到右边

- u - 4 = 3 u - 5

两边加上

4

- u - 4 + 4 = 3 u - 5 + 4

化简

- u = 3 u - 1

- u = 3 u - 1

将

3 u

para o lado esquerdo

- u = 3 u - 1

两边减去

3 u

- u - 3 u = 3 u - 1 - 3 u

化简

- 4 u = - 1

- 4 u = - 1

两边除以

- 4

- 4 u = - 1

两边除以

- 4

\frac{- 4 u}{- 4} = \frac{- 1}{- 4}

化简

u = \frac{1}{4}

u = \frac{1}{4}

u = sin (B)

代回

sin (B) = \frac{1}{4}

sin (B) = \frac{1}{4}

sin (B) = \frac{1}{4} : B = arcsin (\frac{1}{4}) + 2 πn, B = π - arcsin (\frac{1}{4}) + 2 πn

sin (B) = \frac{1}{4}

使用反三角函数性质

sin (B) = \frac{1}{4}

sin (B) = \frac{1}{4}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

B = arcsin (\frac{1}{4}) + 2 πn, B = π - arcsin (\frac{1}{4}) + 2 πn

B = arcsin (\frac{1}{4}) + 2 πn, B = π - arcsin (\frac{1}{4}) + 2 πn

合并所有解

B = arcsin (\frac{1}{4}) + 2 πn, B = π - arcsin (\frac{1}{4}) + 2 πn

以小数形式表示解

B = 0.25268 \dots + 2 πn, B = π - 0.25268 \dots + 2 πn

作图

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