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受欢迎的三角函数 >

0.85=(1-sin(x))/(1+sin(x))

解答

0.85 = \frac{1 - sin ( x )}{1 + sin ( x )}

解答

x = 0.08117 \dots + 2 πn, x = π - 0.08117 \dots + 2 πn

+1

度数

x = 4.65070 \dots^{\circ} + 36 0^{\circ} n, x = 175.34929 \dots^{\circ} + 36 0^{\circ} n

求解步骤

0.85 = \frac{1 - sin ( x )}{1 + sin ( x )}

交换两边

\frac{1 - sin ( x )}{1 + sin ( x )} = 0.85

用替代法求解

\frac{1 - sin ( x )}{1 + sin ( x )} = 0.85

令

: sin (x) = u

\frac{1 - u}{1 + u} = 0.85

\frac{1 - u}{1 + u} = 0.85 : u = \frac{3}{37}

\frac{1 - u}{1 + u} = 0.85

在两边乘以

1 + u

\frac{1 - u}{1 + u} = 0.85

在两边乘以

1 + u

\frac{1 - u}{1 + u} (1 + u) = 0.85 (1 + u)

化简

1 - u = 0.85 (1 + u)

1 - u = 0.85 (1 + u)

在两边乘以

100

1 - u = 0.85 (1 + u)

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

1 \cdot 100 - u \cdot 100 = 0.85 (1 + u) \cdot 100

整理后得

100 - 100 u = 85 (1 + u)

100 - 100 u = 85 (1 + u)

展开

85 (1 + u) : 85 + 85 u

85 (1 + u)

使用分配律:

a (b + c) = ab + a c

a = 85, b = 1, c = u

= 85 \cdot 1 + 85 u

数字相乘:

85 \cdot 1 = 85

= 85 + 85 u

100 - 100 u = 85 + 85 u

将

100

到右边

100 - 100 u = 85 + 85 u

两边减去

100

100 - 100 u - 100 = 85 + 85 u - 100

化简

- 100 u = 85 u - 15

- 100 u = 85 u - 15

将

85 u

para o lado esquerdo

- 100 u = 85 u - 15

两边减去

85 u

- 100 u - 85 u = 85 u - 15 - 85 u

化简

- 185 u = - 15

- 185 u = - 15

两边除以

- 185

- 185 u = - 15

两边除以

- 185

\frac{- 185 u}{- 185} = \frac{- 15}{- 185}

化简

\frac{- 185 u}{- 185} = \frac{- 15}{- 185}

化简

\frac{- 185 u}{- 185} : u

\frac{- 185 u}{- 185}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

= \frac{185 u}{185}

数字相除:

\frac{185}{185} = 1

= u

化简

\frac{- 15}{- 185} : \frac{3}{37}

\frac{- 15}{- 185}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

= \frac{15}{185}

约分:

5

= \frac{3}{37}

u = \frac{3}{37}

u = \frac{3}{37}

u = \frac{3}{37}

验证解

找到无定义的点（奇点）:

u = - 1

取

\frac{1 - u}{1 + u}

的分母，令其等于零

解

1 + u = 0 : u = - 1

1 + u = 0

将

1

到右边

1 + u = 0

两边减去

1

1 + u - 1 = 0 - 1

化简

u = - 1

u = - 1

以下点无定义

u = - 1

将不在定义域的点与解相综合:

u = \frac{3}{37}

u = sin (x)

代回

sin (x) = \frac{3}{37}

sin (x) = \frac{3}{37}

sin (x) = \frac{3}{37} : x = arcsin (\frac{3}{37}) + 2 πn, x = π - arcsin (\frac{3}{37}) + 2 πn

sin (x) = \frac{3}{37}

使用反三角函数性质

sin (x) = \frac{3}{37}

sin (x) = \frac{3}{37}

的通解

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

x = arcsin (\frac{3}{37}) + 2 πn, x = π - arcsin (\frac{3}{37}) + 2 πn

x = arcsin (\frac{3}{37}) + 2 πn, x = π - arcsin (\frac{3}{37}) + 2 πn

合并所有解

x = arcsin (\frac{3}{37}) + 2 πn, x = π - arcsin (\frac{3}{37}) + 2 πn

以小数形式表示解

x = 0.08117 \dots + 2 πn, x = π - 0.08117 \dots + 2 πn

作图

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