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 >

sec((5θ)/4)=2,[0.2pi]

解答

sec (\frac{5 θ}{4}) = 2, [0.2 π]

解答

θ \in R 无解

求解步骤

sec (\frac{5 θ}{4}) = 2, [0.2 π]

sec (\frac{5 θ}{4}) = 2

的通解

sec (x)

周期表（周期为

2 πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

\frac{5 θ}{4} = \frac{π}{3} + 2 πn, \frac{5 θ}{4} = \frac{5 π}{3} + 2 πn

\frac{5 θ}{4} = \frac{π}{3} + 2 πn, \frac{5 θ}{4} = \frac{5 π}{3} + 2 πn

解

\frac{5 θ}{4} = \frac{π}{3} + 2 πn : θ = \frac{4 π}{15} + \frac{8 πn}{5}

\frac{5 θ}{4} = \frac{π}{3} + 2 πn

在两边乘以

4

\frac{5 θ}{4} = \frac{π}{3} + 2 πn

在两边乘以

4

\frac{4 \cdot 5 θ}{4} = 4 \cdot \frac{π}{3} + 4 \cdot 2 πn

化简

\frac{4 \cdot 5 θ}{4} = 4 \cdot \frac{π}{3} + 4 \cdot 2 πn

化简

\frac{4 \cdot 5 θ}{4} : 5 θ

\frac{4 \cdot 5 θ}{4}

数字相乘:

4 \cdot 5 = 20

= \frac{20 θ}{4}

数字相除:

\frac{20}{4} = 5

= 5 θ

化简

4 \cdot \frac{π}{3} + 4 \cdot 2 πn : \frac{4 π}{3} + 8 πn

4 \cdot \frac{π}{3} + 4 \cdot 2 πn

乘

4 \cdot \frac{π}{3} : \frac{4 π}{3}

4 \cdot \frac{π}{3}

分式相乘:

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

= \frac{π 4}{3}

= \frac{4 π}{3} + 4 \cdot 2 πn

数字相乘:

4 \cdot 2 = 8

= \frac{4 π}{3} + 8 πn

5 θ = \frac{4 π}{3} + 8 πn

5 θ = \frac{4 π}{3} + 8 πn

5 θ = \frac{4 π}{3} + 8 πn

两边除以

5

5 θ = \frac{4 π}{3} + 8 πn

两边除以

5

\frac{5 θ}{5} = \frac{\frac{4 π}{3}}{5} + \frac{8 πn}{5}

化简

\frac{5 θ}{5} = \frac{\frac{4 π}{3}}{5} + \frac{8 πn}{5}

化简

\frac{5 θ}{5} : θ

\frac{5 θ}{5}

数字相除:

\frac{5}{5} = 1

= θ

化简

\frac{\frac{4 π}{3}}{5} + \frac{8 πn}{5} : \frac{4 π}{15} + \frac{8 πn}{5}

\frac{\frac{4 π}{3}}{5} + \frac{8 πn}{5}

\frac{\frac{4 π}{3}}{5} = \frac{4 π}{15}

\frac{\frac{4 π}{3}}{5}

使用分式法则:

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

= \frac{4 π}{3 \cdot 5}

数字相乘:

3 \cdot 5 = 15

= \frac{4 π}{15}

= \frac{4 π}{15} + \frac{8 πn}{5}

θ = \frac{4 π}{15} + \frac{8 πn}{5}

θ = \frac{4 π}{15} + \frac{8 πn}{5}

θ = \frac{4 π}{15} + \frac{8 πn}{5}

解

\frac{5 θ}{4} = \frac{5 π}{3} + 2 πn : θ = \frac{4 π}{3} + \frac{8 πn}{5}

\frac{5 θ}{4} = \frac{5 π}{3} + 2 πn

在两边乘以

4

\frac{5 θ}{4} = \frac{5 π}{3} + 2 πn

在两边乘以

4

\frac{4 \cdot 5 θ}{4} = 4 \cdot \frac{5 π}{3} + 4 \cdot 2 πn

化简

\frac{4 \cdot 5 θ}{4} = 4 \cdot \frac{5 π}{3} + 4 \cdot 2 πn

化简

\frac{4 \cdot 5 θ}{4} : 5 θ

\frac{4 \cdot 5 θ}{4}

数字相乘:

4 \cdot 5 = 20

= \frac{20 θ}{4}

数字相除:

\frac{20}{4} = 5

= 5 θ

化简

4 \cdot \frac{5 π}{3} + 4 \cdot 2 πn : \frac{20 π}{3} + 8 πn

4 \cdot \frac{5 π}{3} + 4 \cdot 2 πn

4 \cdot \frac{5 π}{3} = \frac{20 π}{3}

4 \cdot \frac{5 π}{3}

分式相乘:

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

= \frac{5 π 4}{3}

数字相乘:

5 \cdot 4 = 20

= \frac{20 π}{3}

4 \cdot 2 πn = 8 πn

4 \cdot 2 πn

数字相乘:

4 \cdot 2 = 8

= 8 πn

= \frac{20 π}{3} + 8 πn

5 θ = \frac{20 π}{3} + 8 πn

5 θ = \frac{20 π}{3} + 8 πn

5 θ = \frac{20 π}{3} + 8 πn

两边除以

5

5 θ = \frac{20 π}{3} + 8 πn

两边除以

5

\frac{5 θ}{5} = \frac{\frac{20 π}{3}}{5} + \frac{8 πn}{5}

化简

\frac{5 θ}{5} = \frac{\frac{20 π}{3}}{5} + \frac{8 πn}{5}

化简

\frac{5 θ}{5} : θ

\frac{5 θ}{5}

数字相除:

\frac{5}{5} = 1

= θ

化简

\frac{\frac{20 π}{3}}{5} + \frac{8 πn}{5} : \frac{4 π}{3} + \frac{8 πn}{5}

\frac{\frac{20 π}{3}}{5} + \frac{8 πn}{5}

\frac{\frac{20 π}{3}}{5} = \frac{4 π}{3}

\frac{\frac{20 π}{3}}{5}

使用分式法则:

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

= \frac{20 π}{3 \cdot 5}

数字相乘:

3 \cdot 5 = 15

= \frac{20 π}{15}

约分:

5

= \frac{4 π}{3}

= \frac{4 π}{3} + \frac{8 πn}{5}

θ = \frac{4 π}{3} + \frac{8 πn}{5}

θ = \frac{4 π}{3} + \frac{8 πn}{5}

θ = \frac{4 π}{3} + \frac{8 πn}{5}

θ = \frac{4 π}{15} + \frac{8 πn}{5}, θ = \frac{4 π}{3} + \frac{8 πn}{5}

在

[0.2 π]

范围内的解

θ \in R 无解

作图

流行的例子

cos(x)+|cos(x)|=1,-2pi<= x<= 2pi

(30.56)/(sin(88))=(17)/(sin(x))

sec(x+pi/4)=-sqrt(2),-pi<= x<= pi

(56)/((7.071*7.681))=cos(θ)

tan(2x+10)=cot(x-40)