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受欢迎的三角函数 >

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

解答

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

解答

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

+1

度数

x = 4 5^{\circ} + 36 0^{\circ} n, x = 31 5^{\circ} + 36 0^{\circ} n

求解步骤

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

使用三角恒等式改写

- sec (x) + 2 sec (x) cos (x)

sec (x) cos (x) = 1

sec (x) cos (x)

用 sin, cos 表示

sec (x) cos (x)

使用基本三角恒等式:

sec (x) = \frac{1}{cos ( x )}

= \frac{1}{cos ( x )} cos (x)

\frac{1}{cos ( x )} cos (x) = 1

\frac{1}{cos ( x )} cos (x)

分式相乘:

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

= \frac{1 cos ( x )}{cos ( x )}

约分:

cos (x)

= 1

= 1

= - sec (x) + 2 \cdot 1

- sec (x) + 2 \cdot 1 = 0

乘以:

2 \cdot 1 = 2

- sec (x) + 2 = 0

将

2

到右边

- sec (x) + 2 = 0

两边减去

2

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

化简

- sec (x) = - 2

- sec (x) = - 2

两边除以

- 1

- sec (x) = - 2

两边除以

- 1

\frac{- sec ( x )}{- 1} = \frac{- 2}{- 1}

化简

sec (x) = 2

sec (x) = 2

sec (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}

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

作图

流行的例子

2tan(x)-3sin(x)=0

2 tan (x) - 3 sin (x) = 0

sin (x) + 5 = 4

- 9 cos (x) = 0

- 3 cos (x) = 0

4 cot (x) + 2 = 6