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 >

csc(θ/3)=sqrt(6)

解答

csc (\frac{θ}{3}) = 6

解答

θ = 3 \cdot 0.42053 \dots + 6 πn, θ = 3 π - 3 \cdot 0.42053 \dots + 6 πn

+1

度数

θ = 72.28452 \dots^{\circ} + 108 0^{\circ} n, θ = 467.71547 \dots^{\circ} + 108 0^{\circ} n

求解步骤

csc (\frac{θ}{3}) = 6

使用反三角函数性质

csc (\frac{θ}{3}) = 6

csc (\frac{θ}{3}) = 6

的通解

csc (x) = a \Rightarrow x = arccsc (a) + 2 πn, x = π - arccsc (a) + 2 πn

\frac{θ}{3} = arccsc (6) + 2 πn, \frac{θ}{3} = π - arccsc (6) + 2 πn

\frac{θ}{3} = arccsc (6) + 2 πn, \frac{θ}{3} = π - arccsc (6) + 2 πn

解

\frac{θ}{3} = arccsc (6) + 2 πn : θ = 3 arccsc (6) + 6 πn

\frac{θ}{3} = arccsc (6) + 2 πn

在两边乘以

3

\frac{θ}{3} = arccsc (6) + 2 πn

在两边乘以

3

\frac{3 θ}{3} = 3 arccsc (6) + 3 \cdot 2 πn

化简

\frac{3 θ}{3} = 3 arccsc (6) + 3 \cdot 2 πn

化简

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

数字相除:

\frac{3}{3} = 1

= θ

化简

3 arccsc (6) + 3 \cdot 2 πn : 3 arccsc (6) + 6 πn

3 arccsc (6) + 3 \cdot 2 πn

数字相乘:

3 \cdot 2 = 6

= 3 arccsc (6) + 6 πn

θ = 3 arccsc (6) + 6 πn

θ = 3 arccsc (6) + 6 πn

θ = 3 arccsc (6) + 6 πn

解

\frac{θ}{3} = π - arccsc (6) + 2 πn : θ = 3 π - 3 arccsc (6) + 6 πn

\frac{θ}{3} = π - arccsc (6) + 2 πn

在两边乘以

3

\frac{θ}{3} = π - arccsc (6) + 2 πn

在两边乘以

3

\frac{3 θ}{3} = 3 π - 3 arccsc (6) + 3 \cdot 2 πn

化简

\frac{3 θ}{3} = 3 π - 3 arccsc (6) + 3 \cdot 2 πn

化简

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

数字相除:

\frac{3}{3} = 1

= θ

化简

3 π - 3 arccsc (6) + 3 \cdot 2 πn : 3 π - 3 arccsc (6) + 6 πn

3 π - 3 arccsc (6) + 3 \cdot 2 πn

数字相乘:

3 \cdot 2 = 6

= 3 π - 3 arccsc (6) + 6 πn

θ = 3 π - 3 arccsc (6) + 6 πn

θ = 3 π - 3 arccsc (6) + 6 πn

θ = 3 π - 3 arccsc (6) + 6 πn

θ = 3 arccsc (6) + 6 πn, θ = 3 π - 3 arccsc (6) + 6 πn

以小数形式表示解

θ = 3 \cdot 0.42053 \dots + 6 πn, θ = 3 π - 3 \cdot 0.42053 \dots + 6 πn

作图

流行的例子

arcsin (x) = 0

tan (x) = 1.5

tan(3x)=-sqrt(3)

tan (3 x) = - 3

1 = cos (x)

(cot(θ)-1)(2sin(θ)+1)=0

(cot (θ) - 1) (2 sin (θ) + 1) = 0