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受欢迎的三角函数 >

(15)/(sin(32))=(12)/(sin(b))

解答

\frac{15}{sin ( 3 2 ^{\circ} )} = \frac{12}{sin ( b )}

解答

b = 0.43778 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.43778 \dots + 36 0^{\circ} n

+1

弧度

b = 0.43778 \dots + 2 πn, b = π - 0.43778 \dots + 2 πn

求解步骤

\frac{15}{sin ( 3 2 ^{\circ} )} = \frac{12}{sin ( b )}

使用分式交叉相乘

\frac{15}{sin ( 3 2 ^{\circ} )} = \frac{12}{sin ( b )}

使用分式交叉相乘: 若

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

则

a \cdot d = b \cdot c

15 sin (b) = sin (3 2^{\circ}) \cdot 12

15 sin (b) = sin (3 2^{\circ}) \cdot 12

两边除以

15

15 sin (b) = sin (3 2^{\circ}) \cdot 12

两边除以

15

\frac{15 sin ( b )}{15} = \frac{sin ( 3 2 ^{\circ} ) \cdot 12}{15}

化简

sin (b) = \frac{4 sin ( 3 2 ^{\circ} )}{5}

sin (b) = \frac{4 sin ( 3 2 ^{\circ} )}{5}

验证解

找到无定义的点（奇点）:

sin (b) = 0

取

\frac{12}{sin ( b )}

的分母，令其等于零

sin (b) = 0

以下点无定义

sin (b) = 0

将不在定义域的点与解相综合:

sin (b) = \frac{4 sin ( 3 2 ^{\circ} )}{5}

使用反三角函数性质

sin (b) = \frac{4 sin ( 3 2 ^{\circ} )}{5}

sin (b) = \frac{4 sin ( 3 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

b = arcsin (\frac{4 sin ( 3 2 ^{\circ} )}{5}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{4 sin ( 3 2 ^{\circ} )}{5}) + 36 0^{\circ} n

b = arcsin (\frac{4 sin ( 3 2 ^{\circ} )}{5}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{4 sin ( 3 2 ^{\circ} )}{5}) + 36 0^{\circ} n

以小数形式表示解

b = 0.43778 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.43778 \dots + 36 0^{\circ} n

作图

流行的例子

(sin(x))/(25)=(sin(125))/(165.6)

\frac{sin ( x )}{25} = \frac{sin ( 12 5 ^{\circ} )}{165.6}

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cos (4 x) = cos (8 x)

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