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受欢迎的三角函数 >

sec(2x)+sqrt(2)=0

解答

sec (2 x) + 2 = 0

解答

x = \frac{3 π}{8} + πn, x = \frac{5 π}{8} + πn

+1

度数

x = 67. 5^{\circ} + 18 0^{\circ} n, x = 112. 5^{\circ} + 18 0^{\circ} n

求解步骤

sec (2 x) + 2 = 0

将

2

到右边

sec (2 x) + 2 = 0

两边减去

2

sec (2 x) + 2 - 2 = 0 - 2

化简

sec (2 x) = - 2

sec (2 x) = - 2

sec (2 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}

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

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

解

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

2 x = \frac{3 π}{4} + 2 πn

两边除以

2

2 x = \frac{3 π}{4} + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{\frac{3 π}{4}}{2} + \frac{2 πn}{2}

化简

\frac{2 x}{2} = \frac{\frac{3 π}{4}}{2} + \frac{2 πn}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

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

\frac{\frac{3 π}{4}}{2} + \frac{2 πn}{2}

\frac{\frac{3 π}{4}}{2} = \frac{3 π}{8}

\frac{\frac{3 π}{4}}{2}

使用分式法则:

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

= \frac{3 π}{4 \cdot 2}

数字相乘:

4 \cdot 2 = 8

= \frac{3 π}{8}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

= \frac{3 π}{8} + πn

x = \frac{3 π}{8} + πn

x = \frac{3 π}{8} + πn

x = \frac{3 π}{8} + πn

解

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

2 x = \frac{5 π}{4} + 2 πn

两边除以

2

2 x = \frac{5 π}{4} + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{\frac{5 π}{4}}{2} + \frac{2 πn}{2}

化简

\frac{2 x}{2} = \frac{\frac{5 π}{4}}{2} + \frac{2 πn}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

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

\frac{\frac{5 π}{4}}{2} + \frac{2 πn}{2}

\frac{\frac{5 π}{4}}{2} = \frac{5 π}{8}

\frac{\frac{5 π}{4}}{2}

使用分式法则:

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

= \frac{5 π}{4 \cdot 2}

数字相乘:

4 \cdot 2 = 8

= \frac{5 π}{8}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

= \frac{5 π}{8} + πn

x = \frac{5 π}{8} + πn

x = \frac{5 π}{8} + πn

x = \frac{5 π}{8} + πn

x = \frac{3 π}{8} + πn, x = \frac{5 π}{8} + πn

作图

流行的例子

3sin(x+20)-0.75=0

3 sin (x + 2 0^{\circ}) - 0.75 = 0

2sin^2(x)+sin(x)-5=0

2 sin^{2} (x) + sin (x) - 5 = 0

-4sin(x)=4(sin(x)-1)

- 4 sin (x) = 4 (sin (x) - 1)

3/(tan(x))=(2tan(x))(2cos(x))

\frac{3}{tan ( x )} = (2 tan (x)) (2 cos (x))

cos(θ)=-4/5 ,sin(θ)

cos (θ) = - \frac{4}{5}, sin (θ)