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受欢迎的三角函数 >

(30.56)/(sin(88))=(17)/(sin(x))

解答

\frac{30.56}{sin ( 8 8 ^{\circ} )} = \frac{17}{sin ( x )}

解答

x = 0.58949 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.58949 \dots + 36 0^{\circ} n

+1

弧度

x = 0.58949 \dots + 2 πn, x = π - 0.58949 \dots + 2 πn

求解步骤

\frac{30.56}{sin ( 8 8 ^{\circ} )} = \frac{17}{sin ( x )}

使用分式交叉相乘

\frac{30.56}{sin ( 8 8 ^{\circ} )} = \frac{17}{sin ( x )}

使用分式交叉相乘: 若

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

则

a \cdot d = b \cdot c

30.56 sin (x) = sin (8 8^{\circ}) \cdot 17

30.56 sin (x) = sin (8 8^{\circ}) \cdot 17

两边除以

30.56

30.56 sin (x) = sin (8 8^{\circ}) \cdot 17

两边除以

30.56

\frac{30.56 sin ( x )}{30.56} = \frac{sin ( 8 8 ^{\circ} ) \cdot 17}{30.56}

化简

sin (x) = \frac{sin ( 8 8 ^{\circ} ) \cdot 17}{30.56}

sin (x) = \frac{sin ( 8 8 ^{\circ} ) \cdot 17}{30.56}

验证解

找到无定义的点（奇点）:

sin (x) = 0

取

\frac{17}{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{sin ( 8 8 ^{\circ} ) \cdot 17}{30.56}

使用反三角函数性质

sin (x) = \frac{sin ( 8 8 ^{\circ} ) \cdot 17}{30.56}

sin (x) = \frac{sin ( 8 8 ^{\circ} ) 17}{30.56}

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{sin ( 8 8 ^{\circ} ) \cdot 17}{30.56}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 8 8 ^{\circ} ) \cdot 17}{30.56}) + 36 0^{\circ} n

x = arcsin (\frac{sin ( 8 8 ^{\circ} ) \cdot 17}{30.56}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 8 8 ^{\circ} ) \cdot 17}{30.56}) + 36 0^{\circ} n

以小数形式表示解

x = 0.58949 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.58949 \dots + 36 0^{\circ} n

作图

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