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受欢迎的三角函数 >

(12)/(sin(120))= 5/(sin(x))

解答

\frac{12}{sin ( 12 0 ^{\circ} )} = \frac{5}{sin ( x )}

解答

x = 0.36917 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.36917 \dots + 36 0^{\circ} n

+1

弧度

x = 0.36917 \dots + 2 πn, x = π - 0.36917 \dots + 2 πn

求解步骤

\frac{12}{sin ( 12 0 ^{\circ} )} = \frac{5}{sin ( x )}

sin (12 0^{\circ}) = \frac{3}{2}

sin (12 0^{\circ})

使用以下普通恒等式:

sin (12 0^{\circ}) = \frac{3}{2}

sin (12 0^{\circ})

sin (x)

周期表（周期为

36 0^{\circ} n

"）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{3}{2}

= \frac{3}{2}

\frac{12}{\frac{3}{2}} = \frac{5}{sin ( x )}

使用分式交叉相乘

\frac{12}{\frac{3}{2}} = \frac{5}{sin ( x )}

使用分式交叉相乘: 若

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

则

a \cdot d = b \cdot c

12 sin (x) = \frac{3}{2} \cdot 5

化简

\frac{3}{2} \cdot 5 : \frac{5 3}{2}

\frac{3}{2} \cdot 5

分式相乘:

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

= \frac{3 \cdot 5}{2}

12 sin (x) = \frac{5 3}{2}

12 sin (x) = \frac{5 3}{2}

两边除以

12

12 sin (x) = \frac{5 3}{2}

两边除以

12

\frac{12 sin ( x )}{12} = \frac{\frac{5 3}{2}}{12}

化简

\frac{12 sin ( x )}{12} = \frac{\frac{5 3}{2}}{12}

化简

\frac{12 sin ( x )}{12} : sin (x)

\frac{12 sin ( x )}{12}

数字相除:

\frac{12}{12} = 1

= sin (x)

化简

\frac{\frac{5 3}{2}}{12} : \frac{5 3}{24}

\frac{\frac{5 3}{2}}{12}

使用分式法则:

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

= \frac{5 3}{2 \cdot 12}

数字相乘:

2 \cdot 12 = 24

= \frac{5 3}{24}

sin (x) = \frac{5 3}{24}

sin (x) = \frac{5 3}{24}

sin (x) = \frac{5 3}{24}

验证解

找到无定义的点（奇点）:

sin (x) = 0

取

\frac{5}{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 3}{24}

使用反三角函数性质

sin (x) = \frac{5 3}{24}

sin (x) = \frac{5 3}{24}

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 3}{24}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{5 3}{24}) + 36 0^{\circ} n

x = arcsin (\frac{5 3}{24}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{5 3}{24}) + 36 0^{\circ} n

以小数形式表示解

x = 0.36917 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.36917 \dots + 36 0^{\circ} n

作图

流行的例子

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tan (2 θ) = - \frac{2}{5}

cos(2x)-3cos(x)=-2

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cos^2(3x)=cos(9x^2)

cos^{2} (3 x) = cos (9 x^{2})