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受欢迎的三角函数 >

sec(5x)=2

解答

sec (5 x) = 2

解答

x = \frac{π}{15} + \frac{2 πn}{5}, x = \frac{π}{3} + \frac{2 πn}{5}

+1

度数

x = 1 2^{\circ} + 7 2^{\circ} n, x = 6 0^{\circ} + 7 2^{\circ} n

求解步骤

sec (5 x) = 2

sec (5 x) = 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 x = \frac{π}{3} + 2 πn, 5 x = \frac{5 π}{3} + 2 πn

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

解

5 x = \frac{π}{3} + 2 πn : x = \frac{π}{15} + \frac{2 πn}{5}

5 x = \frac{π}{3} + 2 πn

两边除以

5

5 x = \frac{π}{3} + 2 πn

两边除以

5

\frac{5 x}{5} = \frac{\frac{π}{3}}{5} + \frac{2 πn}{5}

化简

\frac{5 x}{5} = \frac{\frac{π}{3}}{5} + \frac{2 πn}{5}

化简

\frac{5 x}{5} : x

\frac{5 x}{5}

数字相除:

\frac{5}{5} = 1

= x

化简

\frac{\frac{π}{3}}{5} + \frac{2 πn}{5} : \frac{π}{15} + \frac{2 πn}{5}

\frac{\frac{π}{3}}{5} + \frac{2 πn}{5}

\frac{\frac{π}{3}}{5} = \frac{π}{15}

\frac{\frac{π}{3}}{5}

使用分式法则:

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

= \frac{π}{3 \cdot 5}

数字相乘:

3 \cdot 5 = 15

= \frac{π}{15}

= \frac{π}{15} + \frac{2 πn}{5}

x = \frac{π}{15} + \frac{2 πn}{5}

x = \frac{π}{15} + \frac{2 πn}{5}

x = \frac{π}{15} + \frac{2 πn}{5}

解

5 x = \frac{5 π}{3} + 2 πn : x = \frac{π}{3} + \frac{2 πn}{5}

5 x = \frac{5 π}{3} + 2 πn

两边除以

5

5 x = \frac{5 π}{3} + 2 πn

两边除以

5

\frac{5 x}{5} = \frac{\frac{5 π}{3}}{5} + \frac{2 πn}{5}

化简

\frac{5 x}{5} = \frac{\frac{5 π}{3}}{5} + \frac{2 πn}{5}

化简

\frac{5 x}{5} : x

\frac{5 x}{5}

数字相除:

\frac{5}{5} = 1

= x

化简

\frac{\frac{5 π}{3}}{5} + \frac{2 πn}{5} : \frac{π}{3} + \frac{2 πn}{5}

\frac{\frac{5 π}{3}}{5} + \frac{2 πn}{5}

\frac{\frac{5 π}{3}}{5} = \frac{π}{3}

\frac{\frac{5 π}{3}}{5}

使用分式法则:

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

= \frac{5 π}{3 \cdot 5}

数字相乘:

3 \cdot 5 = 15

= \frac{5 π}{15}

约分:

5

= \frac{π}{3}

= \frac{π}{3} + \frac{2 πn}{5}

x = \frac{π}{3} + \frac{2 πn}{5}

x = \frac{π}{3} + \frac{2 πn}{5}

x = \frac{π}{3} + \frac{2 πn}{5}

x = \frac{π}{15} + \frac{2 πn}{5}, x = \frac{π}{3} + \frac{2 πn}{5}

作图

流行的例子

5sin(θ)-1=3sin(θ)

5 sin (θ) - 1 = 3 sin (θ)

2cos^2(w)-cos(w)-1=0

2 cos^{2} (w) - cos (w) - 1 = 0

3 csc (θ) - 3 = 0

2sin(x)+(sin(x))^2=0

2 sin (x) + (sin (x))^{2} = 0

1 - 2 sin (2 x) = 0