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受欢迎的三角函数 >

(87.17)/(sin(120))=(40)/(sin(x))

解答

\frac{87.17}{sin ( 12 0 ^{\circ} )} = \frac{40}{sin ( x )}

解答

x = 0.40867 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.40867 \dots + 36 0^{\circ} n

+1

弧度

x = 0.40867 \dots + 2 πn, x = π - 0.40867 \dots + 2 πn

求解步骤

\frac{87.17}{sin ( 12 0 ^{\circ} )} = \frac{40}{sin ( x )}

sin (12 0^{\circ}) = \frac{3}{2}

sin (12 0^{\circ})

使用以下普通恒等式:

sin (12 0^{\circ}) = \frac{3}{2}

sin (12 0^{\circ})

sin (x)

周期表（周期为

36 0^{\circ} n

"）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{3}{2}

= \frac{3}{2}

\frac{87.17}{\frac{3}{2}} = \frac{40}{sin ( x )}

使用分式交叉相乘

\frac{87.17}{\frac{3}{2}} = \frac{40}{sin ( x )}

使用分式交叉相乘: 若

\frac{a}{b} = \frac{c}{d}

则

a \cdot d = b \cdot c

87.17 sin (x) = \frac{3}{2} \cdot 40

化简

\frac{3}{2} \cdot 40 : 203

\frac{3}{2} \cdot 40

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 \cdot 40}{2}

数字相除:

\frac{40}{2} = 20

= 203

87.17 sin (x) = 203

87.17 sin (x) = 203

在两边乘以

100

87.17 sin (x) = 203

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

87.17 sin (x) \cdot 100 = 203 \cdot 100

整理后得

8717 sin (x) = 20003

8717 sin (x) = 20003

两边除以

8717

8717 sin (x) = 20003

两边除以

8717

\frac{8717 sin ( x )}{8717} = \frac{2000 3}{8717}

化简

sin (x) = \frac{2000 3}{8717}

sin (x) = \frac{2000 3}{8717}

验证解

找到无定义的点（奇点）:

sin (x) = 0

取

\frac{40}{sin ( x )}

的分母，令其等于零

sin (x) = 0

以下点无定义

sin (x) = 0

将不在定义域的点与解相综合:

sin (x) = \frac{2000 3}{8717}

使用反三角函数性质

sin (x) = \frac{2000 3}{8717}

sin (x) = \frac{2000 3}{8717}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x = arcsin (\frac{2000 3}{8717}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{2000 3}{8717}) + 36 0^{\circ} n

x = arcsin (\frac{2000 3}{8717}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{2000 3}{8717}) + 36 0^{\circ} n

以小数形式表示解

x = 0.40867 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.40867 \dots + 36 0^{\circ} n

作图

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