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受欢迎的三角函数 >

4/(sin(104.48))= 2/(sin(a))

解答

\frac{4}{sin ( 104.4 8 ^{\circ} )} = \frac{2}{sin ( a )}

解答

a = 0.50535 \dots + 36 0^{\circ} n, a = 18 0^{\circ} - 0.50535 \dots + 36 0^{\circ} n

+1

弧度

a = 0.50535 \dots + 2 πn, a = π - 0.50535 \dots + 2 πn

求解步骤

\frac{4}{sin ( 104.4 8 ^{\circ} )} = \frac{2}{sin ( a )}

使用分式交叉相乘

\frac{4}{sin ( 104.4 8 ^{\circ} )} = \frac{2}{sin ( a )}

使用分式交叉相乘: 若

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

则

a \cdot d = b \cdot c

4 sin (a) = sin (104.4 8^{\circ}) \cdot 2

4 sin (a) = sin (104.4 8^{\circ}) \cdot 2

两边除以

4

4 sin (a) = sin (104.4 8^{\circ}) \cdot 2

两边除以

4

\frac{4 sin ( a )}{4} = \frac{sin ( 104.4 8 ^{\circ} ) \cdot 2}{4}

化简

sin (a) = \frac{sin ( 104.4 8 ^{\circ} )}{2}

sin (a) = \frac{sin ( 104.4 8 ^{\circ} )}{2}

验证解

找到无定义的点（奇点）:

sin (a) = 0

取

\frac{2}{sin ( a )}

的分母，令其等于零

sin (a) = 0

以下点无定义

sin (a) = 0

将不在定义域的点与解相综合:

sin (a) = \frac{sin ( 104.4 8 ^{\circ} )}{2}

使用反三角函数性质

sin (a) = \frac{sin ( 104.4 8 ^{\circ} )}{2}

sin (a) = \frac{sin ( 104.4 8 ^{\circ} )}{2}

的通解

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

a = arcsin (\frac{sin ( 104.4 8 ^{\circ} )}{2}) + 36 0^{\circ} n, a = 18 0^{\circ} - arcsin (\frac{sin ( 104.4 8 ^{\circ} )}{2}) + 36 0^{\circ} n

a = arcsin (\frac{sin ( 104.4 8 ^{\circ} )}{2}) + 36 0^{\circ} n, a = 18 0^{\circ} - arcsin (\frac{sin ( 104.4 8 ^{\circ} )}{2}) + 36 0^{\circ} n

以小数形式表示解

a = 0.50535 \dots + 36 0^{\circ} n, a = 18 0^{\circ} - 0.50535 \dots + 36 0^{\circ} n

作图

流行的例子

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cot (2 x) = 1.732

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