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受欢迎的三角函数 >

(26)/(sin(88))=(21)/(sin(c))

解答

\frac{26}{sin ( 8 8 ^{\circ} )} = \frac{21}{sin ( c )}

解答

c = 0.93939 \dots + 36 0^{\circ} n, c = 18 0^{\circ} - 0.93939 \dots + 36 0^{\circ} n

+1

弧度

c = 0.93939 \dots + 2 πn, c = π - 0.93939 \dots + 2 πn

求解步骤

\frac{26}{sin ( 8 8 ^{\circ} )} = \frac{21}{sin ( c )}

使用分式交叉相乘

\frac{26}{sin ( 8 8 ^{\circ} )} = \frac{21}{sin ( c )}

使用分式交叉相乘: 若

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

则

a \cdot d = b \cdot c

26 sin (c) = sin (8 8^{\circ}) \cdot 21

26 sin (c) = sin (8 8^{\circ}) \cdot 21

两边除以

26

26 sin (c) = sin (8 8^{\circ}) \cdot 21

两边除以

26

\frac{26 sin ( c )}{26} = \frac{sin ( 8 8 ^{\circ} ) \cdot 21}{26}

化简

sin (c) = \frac{sin ( 8 8 ^{\circ} ) \cdot 21}{26}

sin (c) = \frac{sin ( 8 8 ^{\circ} ) \cdot 21}{26}

验证解

找到无定义的点（奇点）:

sin (c) = 0

取

\frac{21}{sin ( c )}

的分母，令其等于零

sin (c) = 0

以下点无定义

sin (c) = 0

将不在定义域的点与解相综合:

sin (c) = \frac{sin ( 8 8 ^{\circ} ) \cdot 21}{26}

使用反三角函数性质

sin (c) = \frac{sin ( 8 8 ^{\circ} ) \cdot 21}{26}

sin (c) = \frac{sin ( 8 8 ^{\circ} ) 21}{26}

的通解

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

c = arcsin (\frac{sin ( 8 8 ^{\circ} ) \cdot 21}{26}) + 36 0^{\circ} n, c = 18 0^{\circ} - arcsin (\frac{sin ( 8 8 ^{\circ} ) \cdot 21}{26}) + 36 0^{\circ} n

c = arcsin (\frac{sin ( 8 8 ^{\circ} ) \cdot 21}{26}) + 36 0^{\circ} n, c = 18 0^{\circ} - arcsin (\frac{sin ( 8 8 ^{\circ} ) \cdot 21}{26}) + 36 0^{\circ} n

以小数形式表示解

c = 0.93939 \dots + 36 0^{\circ} n, c = 18 0^{\circ} - 0.93939 \dots + 36 0^{\circ} n

作图

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