zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

8/(sin(45))=(42)/(sin(x))

解答

\frac{8}{sin ( 4 5 ^{\circ} )} = \frac{42}{sin ( x )}

解答

x \in R 无解

求解步骤

\frac{8}{sin ( 4 5 ^{\circ} )} = \frac{42}{sin ( x )}

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

sin (4 5^{\circ})

使用以下普通恒等式:

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

sin (4 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{8}{\frac{2}{2}} = \frac{42}{sin ( x )}

使用分式交叉相乘

\frac{8}{\frac{2}{2}} = \frac{42}{sin ( x )}

使用分式交叉相乘: 若

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

则

a \cdot d = b \cdot c

8 sin (x) = \frac{2}{2} \cdot 42

化简

\frac{2}{2} \cdot 42 : 212

\frac{2}{2} \cdot 42

分式相乘:

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

= \frac{2 \cdot 42}{2}

数字相除:

\frac{42}{2} = 21

= 212

8 sin (x) = 212

8 sin (x) = 212

两边除以

8

8 sin (x) = 212

两边除以

8

\frac{8 sin ( x )}{8} = \frac{21 2}{8}

化简

sin (x) = \frac{21 2}{8}

sin (x) = \frac{21 2}{8}

验证解

找到无定义的点（奇点）:

sin (x) = 0

取

\frac{42}{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{21 2}{8}

- 1 \leq sin (x) \leq 1

x \in R 无解

作图

流行的例子

-2cos^2(4x)+2sin(4x)-1=0

- 2 cos^{2} (4 x) + 2 sin (4 x) - 1 = 0

cos(θ)=(sqrt(75))/(10)

cos (θ) = \frac{75}{10}

tan (x) = \frac{50}{30}

cos(A)=(1^2+5.2^2-3.5)/(2(1)(5.2))

cos (A) = \frac{1 ^{2} + 5. 2 ^{2} - 3.5}{2 ( 1 ) ( 5.2 )}

cos(5x)-cos(3x)=sin(4x)

cos (5 x) - cos (3 x) = sin (4 x)