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受欢迎的三角函数 >

(35)/(sin(A))=(60)/(sin(25))

解答

\frac{35}{sin ( A )} = \frac{60}{sin ( 2 5 ^{\circ} )}

解答

A = 0.24909 \dots + 36 0^{\circ} n, A = 18 0^{\circ} - 0.24909 \dots + 36 0^{\circ} n

+1

弧度

A = 0.24909 \dots + 2 πn, A = π - 0.24909 \dots + 2 πn

求解步骤

\frac{35}{sin ( A )} = \frac{60}{sin ( 2 5 ^{\circ} )}

使用分式交叉相乘

\frac{35}{sin ( A )} = \frac{60}{sin ( 2 5 ^{\circ} )}

使用分式交叉相乘: 若

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

则

a \cdot d = b \cdot c

35 sin (2 5^{\circ}) = sin (A) \cdot 60

35 sin (2 5^{\circ}) = sin (A) \cdot 60

交换两边

sin (A) \cdot 60 = 35 sin (2 5^{\circ})

两边除以

60

sin (A) \cdot 60 = 35 sin (2 5^{\circ})

两边除以

60

\frac{sin ( A ) \cdot 60}{60} = \frac{35 sin ( 2 5 ^{\circ} )}{60}

化简

sin (A) = \frac{7 sin ( 2 5 ^{\circ} )}{12}

sin (A) = \frac{7 sin ( 2 5 ^{\circ} )}{12}

验证解

找到无定义的点（奇点）:

sin (A) = 0

取

\frac{35}{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{7 sin ( 2 5 ^{\circ} )}{12}

使用反三角函数性质

sin (A) = \frac{7 sin ( 2 5 ^{\circ} )}{12}

sin (A) = \frac{7 sin ( 2 5 ^{\circ} )}{12}

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{7 sin ( 2 5 ^{\circ} )}{12}) + 36 0^{\circ} n, A = 18 0^{\circ} - arcsin (\frac{7 sin ( 2 5 ^{\circ} )}{12}) + 36 0^{\circ} n

A = arcsin (\frac{7 sin ( 2 5 ^{\circ} )}{12}) + 36 0^{\circ} n, A = 18 0^{\circ} - arcsin (\frac{7 sin ( 2 5 ^{\circ} )}{12}) + 36 0^{\circ} n

以小数形式表示解

A = 0.24909 \dots + 36 0^{\circ} n, A = 18 0^{\circ} - 0.24909 \dots + 36 0^{\circ} n

作图

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