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(5 θ/4)=2,0<θ<2pi

解答

sec (5 \frac{θ}{4}) = 2, 0 < θ < 2 π

解答

θ = \frac{4 π}{15}, θ = \frac{4 π}{3}, θ = \frac{28 π}{15}

+1

度数

θ = 4 8^{\circ}, θ = 24 0^{\circ}, θ = 33 6^{\circ}

求解步骤

sec (5 \cdot \frac{θ}{4}) = 2, 0 < θ < 2 π

sec (5 \frac{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}

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

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

解

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

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

整理

5 \cdot \frac{θ}{4} : \frac{5 θ}{4}

5 \cdot \frac{θ}{4}

分式相乘:

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

= \frac{θ \cdot 5}{4}

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

化简

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

化简

\frac{5 θ}{4} \cdot 4 : 5 θ

\frac{5 θ}{4} \cdot 4

分式相乘:

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

= \frac{5 θ \cdot 4}{4}

约分:

4

= 5 θ

化简

\frac{π}{3} \cdot 4 : \frac{4 π}{3}

\frac{π}{3} \cdot 4

分式相乘:

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

= \frac{π 4}{3}

化简

2 πn \cdot 4 : 8 πn

2 πn \cdot 4

数字相乘:

2 \cdot 4 = 8

= 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

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

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

整理

5 \cdot \frac{θ}{4} : \frac{5 θ}{4}

5 \cdot \frac{θ}{4}

分式相乘:

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

= \frac{θ \cdot 5}{4}

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

化简

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

化简

\frac{5 θ}{4} \cdot 4 : 5 θ

\frac{5 θ}{4} \cdot 4

分式相乘:

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

= \frac{5 θ \cdot 4}{4}

约分:

4

= 5 θ

化简

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

\frac{5 π}{3} \cdot 4

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}

化简

2 πn \cdot 4 : 8 πn

2 πn \cdot 4

数字相乘:

2 \cdot 4 = 8

= 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 < θ < 2 π

范围内的解

θ = \frac{4 π}{15}, θ = \frac{4 π}{3}, θ = \frac{28 π}{15}

作图

流行的例子

2 sin (\frac{x}{2}) = 1

sin^2(x)-3cos^2(x)=0

sin^{2} (x) - 3 cos^{2} (x) = 0

cos(2x+pi/3)=sin(3x)

cos (2 x + \frac{π}{3}) = sin (3 x)

solvefor y,x=arcsin(y)

so l v e f or y, x = arcsin (y)

2sin^2(x)+5sin(x)=3

2 sin^{2} (x) + 5 sin (x) = 3