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受欢迎的三角函数 >

(125)/(sin(110))=(100)/(sin(b))

解答

\frac{125}{sin ( 11 0 ^{\circ} )} = \frac{100}{sin ( b )}

解答

b = 0.85071 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.85071 \dots + 36 0^{\circ} n

+1

弧度

b = 0.85071 \dots + 2 πn, b = π - 0.85071 \dots + 2 πn

求解步骤

\frac{125}{sin ( 11 0 ^{\circ} )} = \frac{100}{sin ( b )}

使用分式交叉相乘

\frac{125}{sin ( 11 0 ^{\circ} )} = \frac{100}{sin ( b )}

使用分式交叉相乘: 若

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

则

a \cdot d = b \cdot c

125 sin (b) = sin (11 0^{\circ}) \cdot 100

125 sin (b) = sin (11 0^{\circ}) \cdot 100

两边除以

125

125 sin (b) = sin (11 0^{\circ}) \cdot 100

两边除以

125

\frac{125 sin ( b )}{125} = \frac{sin ( 11 0 ^{\circ} ) \cdot 100}{125}

化简

sin (b) = \frac{4 sin ( 11 0 ^{\circ} )}{5}

sin (b) = \frac{4 sin ( 11 0 ^{\circ} )}{5}

验证解

找到无定义的点（奇点）:

sin (b) = 0

取

\frac{100}{sin ( b )}

的分母，令其等于零

sin (b) = 0

以下点无定义

sin (b) = 0

将不在定义域的点与解相综合:

sin (b) = \frac{4 sin ( 11 0 ^{\circ} )}{5}

使用反三角函数性质

sin (b) = \frac{4 sin ( 11 0 ^{\circ} )}{5}

sin (b) = \frac{4 sin ( 11 0 ^{\circ} )}{5}

的通解

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

b = arcsin (\frac{4 sin ( 11 0 ^{\circ} )}{5}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{4 sin ( 11 0 ^{\circ} )}{5}) + 36 0^{\circ} n

b = arcsin (\frac{4 sin ( 11 0 ^{\circ} )}{5}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{4 sin ( 11 0 ^{\circ} )}{5}) + 36 0^{\circ} n

以小数形式表示解

b = 0.85071 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.85071 \dots + 36 0^{\circ} n

作图

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