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受欢迎的三角函数 >

(sin(82))/(sin(x))=sqrt(5)

解答

\frac{sin ( 8 2 ^{\circ} )}{sin ( x )} = 5

解答

x = 0.45878 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.45878 \dots + 36 0^{\circ} n

+1

弧度

x = 0.45878 \dots + 2 πn, x = π - 0.45878 \dots + 2 πn

求解步骤

\frac{sin ( 8 2 ^{\circ} )}{sin ( x )} = 5

在两边乘以

sin (x)

\frac{sin ( 8 2 ^{\circ} )}{sin ( x )} = 5

在两边乘以

sin (x)

\frac{sin ( 8 2 ^{\circ} )}{sin ( x )} sin (x) = 5 sin (x)

化简

sin (8 2^{\circ}) = 5 sin (x)

sin (8 2^{\circ}) = 5 sin (x)

交换两边

5 sin (x) = sin (8 2^{\circ})

两边除以

5

5 sin (x) = sin (8 2^{\circ})

两边除以

5

\frac{5 sin ( x )}{5} = \frac{sin ( 8 2 ^{\circ} )}{5}

化简

\frac{5 sin ( x )}{5} = \frac{sin ( 8 2 ^{\circ} )}{5}

化简

\frac{5 sin ( x )}{5} : sin (x)

\frac{5 sin ( x )}{5}

约分:

5

= sin (x)

化简

\frac{sin ( 8 2 ^{\circ} )}{5} : \frac{5 sin ( 8 2 ^{\circ} )}{5}

\frac{sin ( 8 2 ^{\circ} )}{5}

乘以共轭根式

\frac{5}{5}

= \frac{sin ( 8 2 ^{\circ} ) 5}{5 5}

55 = 5

55

使用根式运算法则:

a a = a

55 = 5

= 5

= \frac{5 sin ( 8 2 ^{\circ} )}{5}

sin (x) = \frac{5 sin ( 8 2 ^{\circ} )}{5}

sin (x) = \frac{5 sin ( 8 2 ^{\circ} )}{5}

sin (x) = \frac{5 sin ( 8 2 ^{\circ} )}{5}

验证解

找到无定义的点（奇点）:

sin (x) = 0

取

\frac{sin ( 8 2 ^{\circ} )}{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{5 sin ( 8 2 ^{\circ} )}{5}

使用反三角函数性质

sin (x) = \frac{5 sin ( 8 2 ^{\circ} )}{5}

sin (x) = \frac{5 sin ( 8 2 ^{\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

x = arcsin (\frac{5 sin ( 8 2 ^{\circ} )}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{5 sin ( 8 2 ^{\circ} )}{5}) + 36 0^{\circ} n

x = arcsin (\frac{5 sin ( 8 2 ^{\circ} )}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{5 sin ( 8 2 ^{\circ} )}{5}) + 36 0^{\circ} n

以小数形式表示解

x = 0.45878 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.45878 \dots + 36 0^{\circ} n

作图

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