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 >

(408.4)/(sin(130))=(200)/(sin(x))

解答

\frac{408.4}{sin ( 13 0 ^{\circ} )} = \frac{200}{sin ( x )}

解答

x = 0.38455 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.38455 \dots + 36 0^{\circ} n

+1

弧度

x = 0.38455 \dots + 2 πn, x = π - 0.38455 \dots + 2 πn

求解步骤

\frac{408.4}{sin ( 13 0 ^{\circ} )} = \frac{200}{sin ( x )}

使用分式交叉相乘

\frac{408.4}{sin ( 13 0 ^{\circ} )} = \frac{200}{sin ( x )}

使用分式交叉相乘: 若

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

则

a \cdot d = b \cdot c

408.4 sin (x) = sin (13 0^{\circ}) \cdot 200

408.4 sin (x) = sin (13 0^{\circ}) \cdot 200

两边除以

408.4

408.4 sin (x) = sin (13 0^{\circ}) \cdot 200

两边除以

408.4

\frac{408.4 sin ( x )}{408.4} = \frac{sin ( 13 0 ^{\circ} ) \cdot 200}{408.4}

化简

sin (x) = \frac{sin ( 13 0 ^{\circ} ) \cdot 200}{408.4}

sin (x) = \frac{sin ( 13 0 ^{\circ} ) \cdot 200}{408.4}

验证解

找到无定义的点（奇点）:

sin (x) = 0

取

\frac{200}{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{sin ( 13 0 ^{\circ} ) \cdot 200}{408.4}

使用反三角函数性质

sin (x) = \frac{sin ( 13 0 ^{\circ} ) \cdot 200}{408.4}

sin (x) = \frac{sin ( 13 0 ^{\circ} ) 200}{408.4}

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{sin ( 13 0 ^{\circ} ) \cdot 200}{408.4}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 13 0 ^{\circ} ) \cdot 200}{408.4}) + 36 0^{\circ} n

x = arcsin (\frac{sin ( 13 0 ^{\circ} ) \cdot 200}{408.4}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 13 0 ^{\circ} ) \cdot 200}{408.4}) + 36 0^{\circ} n

以小数形式表示解

x = 0.38455 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.38455 \dots + 36 0^{\circ} n

作图

流行的例子

cot (θ) = - \frac{7}{6}

2/pi arccos(m*1-1)=0

\frac{2}{π} arccos (m \cdot 1 - 1) = 0

sin(θ)cos(θ)-1/2 cos(θ)=0

sin (θ) cos (θ) - \frac{1}{2} cos (θ) = 0

cos^2(60)+cos^2(45)+cos^2(x)=1

cos^{2} (60) + cos^{2} (45) + cos^{2} (x) = 1

3sin(5x)=-1,x<2pi,0

3 sin (5 x) = - 1, x < 2 π, 0