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 >

(29)/(sin(50))=(37)/(sin(x))

解答

\frac{29}{sin ( 5 0 ^{\circ} )} = \frac{37}{sin ( x )}

解答

x = 1.35763 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.35763 \dots + 36 0^{\circ} n

+1

弧度

x = 1.35763 \dots + 2 πn, x = π - 1.35763 \dots + 2 πn

求解步骤

\frac{29}{sin ( 5 0 ^{\circ} )} = \frac{37}{sin ( x )}

使用分式交叉相乘

\frac{29}{sin ( 5 0 ^{\circ} )} = \frac{37}{sin ( x )}

使用分式交叉相乘: 若

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

则

a \cdot d = b \cdot c

29 sin (x) = sin (5 0^{\circ}) \cdot 37

29 sin (x) = sin (5 0^{\circ}) \cdot 37

两边除以

29

29 sin (x) = sin (5 0^{\circ}) \cdot 37

两边除以

29

\frac{29 sin ( x )}{29} = \frac{sin ( 5 0 ^{\circ} ) \cdot 37}{29}

化简

sin (x) = \frac{sin ( 5 0 ^{\circ} ) \cdot 37}{29}

sin (x) = \frac{sin ( 5 0 ^{\circ} ) \cdot 37}{29}

验证解

找到无定义的点（奇点）:

sin (x) = 0

取

\frac{37}{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 ( 5 0 ^{\circ} ) \cdot 37}{29}

使用反三角函数性质

sin (x) = \frac{sin ( 5 0 ^{\circ} ) \cdot 37}{29}

sin (x) = \frac{sin ( 5 0 ^{\circ} ) 37}{29}

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 ( 5 0 ^{\circ} ) \cdot 37}{29}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 5 0 ^{\circ} ) \cdot 37}{29}) + 36 0^{\circ} n

x = arcsin (\frac{sin ( 5 0 ^{\circ} ) \cdot 37}{29}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 5 0 ^{\circ} ) \cdot 37}{29}) + 36 0^{\circ} n

以小数形式表示解

x = 1.35763 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.35763 \dots + 36 0^{\circ} n

作图

流行的例子

arccos (θ) = 1.6

sin(90-θ)=0.5745

sin (9 0^{\circ} - θ) = 0.5745

sin (x) = \frac{60}{61}

solvefor a,tan(a)=3

so l v e f or a, tan (a) = 3

2cos(12x)=sqrt(3)

2 cos (12 x) = 3