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 >

csc(x)+cot(x)=0

解答

csc (x) + cot (x) = 0

解答

x \in R 无解

求解步骤

csc (x) + cot (x) = 0

用 sin, cos 表示

cot (x) + csc (x)

使用基本三角恒等式:

cot (x) = \frac{cos ( x )}{sin ( x )}

= \frac{cos ( x )}{sin ( x )} + csc (x)

使用基本三角恒等式:

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

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

化简

\frac{cos ( x )}{sin ( x )} + \frac{1}{sin ( x )} : \frac{cos ( x ) + 1}{sin ( x )}

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

使用法则

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

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

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

\frac{1 + cos ( x )}{sin ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

1 + cos (x) = 0

将

1

到右边

1 + cos (x) = 0

两边减去

1

1 + cos (x) - 1 = 0 - 1

化简

cos (x) = - 1

cos (x) = - 1

cos (x) = - 1

的通解

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} 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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = π + 2 πn

x = π + 2 πn

因为方程对以下值无定义:

π + 2 πn

x \in R 无解

作图

流行的例子

cos^2(θ)-sin^2(θ)=0

cos^{2} (θ) - sin^{2} (θ) = 0

7=4sin(pi/2 (x-2))+5

7 = 4 sin (\frac{π}{2} (x - 2)) + 5

5 - cos (θ) = 5

6sin(θ)=2+2sin(θ)

6 sin (θ) = 2 + 2 sin (θ)

sin(x-pi/4)-sin(x+pi/4)=0.25

sin (x - \frac{π}{4}) - sin (x + \frac{π}{4}) = 0.25