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受欢迎的三角函数 >

10sin(x)+1=3-2sin(x)

解答

10 sin (x) + 1 = 3 - 2 sin (x)

解答

x = 0.16744 \dots + 2 πn, x = π - 0.16744 \dots + 2 πn

+1

度数

x = 9.59406 \dots^{\circ} + 36 0^{\circ} n, x = 170.40593 \dots^{\circ} + 36 0^{\circ} n

求解步骤

10 sin (x) + 1 = 3 - 2 sin (x)

用替代法求解

10 sin (x) + 1 = 3 - 2 sin (x)

令

: sin (x) = u

10 u + 1 = 3 - 2 u

10 u + 1 = 3 - 2 u : u = \frac{1}{6}

10 u + 1 = 3 - 2 u

将

1

到右边

10 u + 1 = 3 - 2 u

两边减去

1

10 u + 1 - 1 = 3 - 2 u - 1

化简

10 u = - 2 u + 2

10 u = - 2 u + 2

将

2 u

para o lado esquerdo

10 u = - 2 u + 2

两边加上

2 u

10 u + 2 u = - 2 u + 2 + 2 u

化简

12 u = 2

12 u = 2

两边除以

12

12 u = 2

两边除以

12

\frac{12 u}{12} = \frac{2}{12}

化简

u = \frac{1}{6}

u = \frac{1}{6}

u = sin (x)

代回

sin (x) = \frac{1}{6}

sin (x) = \frac{1}{6}

sin (x) = \frac{1}{6} : x = arcsin (\frac{1}{6}) + 2 πn, x = π - arcsin (\frac{1}{6}) + 2 πn

sin (x) = \frac{1}{6}

使用反三角函数性质

sin (x) = \frac{1}{6}

sin (x) = \frac{1}{6}

的通解

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

x = arcsin (\frac{1}{6}) + 2 πn, x = π - arcsin (\frac{1}{6}) + 2 πn

x = arcsin (\frac{1}{6}) + 2 πn, x = π - arcsin (\frac{1}{6}) + 2 πn

合并所有解

x = arcsin (\frac{1}{6}) + 2 πn, x = π - arcsin (\frac{1}{6}) + 2 πn

以小数形式表示解

x = 0.16744 \dots + 2 πn, x = π - 0.16744 \dots + 2 πn

作图

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