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受欢迎的三角函数 >

2/3 =(sin(135))/(sin(x))

解答

\frac{2}{3} = \frac{sin ( 13 5 ^{\circ} )}{sin ( x )}

解答

x \in R 无解

求解步骤

\frac{2}{3} = \frac{sin ( 13 5 ^{\circ} )}{sin ( x )}

交换两边

\frac{sin ( 13 5 ^{\circ} )}{sin ( x )} = \frac{2}{3}

sin (13 5^{\circ}) = \frac{2}{2}

sin (13 5^{\circ})

使用以下普通恒等式:

sin (13 5^{\circ}) = \frac{2}{2}

sin (13 5^{\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{2}{2}

= \frac{2}{2}

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

使用分式交叉相乘

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

化简

\frac{\frac{2}{2}}{sin ( x )} : \frac{2}{2 sin ( x )}

\frac{\frac{2}{2}}{sin ( x )}

使用分式法则:

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

= \frac{2}{2 sin ( x )}

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

使用分式交叉相乘: 若

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

则

a \cdot d = b \cdot c

2 \cdot 3 = 2 sin (x) \cdot 2

化简

2 sin (x) \cdot 2 : 4 sin (x)

2 sin (x) \cdot 2

数字相乘:

2 \cdot 2 = 4

= 4 sin (x)

2 \cdot 3 = 4 sin (x)

2 \cdot 3 = 4 sin (x)

交换两边

4 sin (x) = 2 \cdot 3

两边除以

4

4 sin (x) = 2 \cdot 3

两边除以

4

\frac{4 sin ( x )}{4} = \frac{2 \cdot 3}{4}

化简

sin (x) = \frac{2 \cdot 3}{4}

sin (x) = \frac{2 \cdot 3}{4}

验证解

找到无定义的点（奇点）:

sin (x) = 0

取

\frac{\frac{2}{2}}{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{2 \cdot 3}{4}

- 1 \leq sin (x) \leq 1

x \in R 无解

作图

流行的例子

10 = cos (x)

tan (θ) = \frac{0}{5}

3 tan (x^{2}) - 1 = 0

sin(θ)=(sqrt(58))/8

sin (θ) = \frac{58}{8}

cos (θ) = - 0.6