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受欢迎的三角函数 >

(csc(x))=-csc(x)cot(x)

解答

(csc (x)) = - csc (x) cot (x)

解答

x = \frac{3 π}{4} + πn

+1

度数

x = 13 5^{\circ} + 18 0^{\circ} n

求解步骤

(csc (x)) = - csc (x) cot (x)

两边减去

- csc (x) cot (x)

csc (x) + csc (x) cot (x) = 0

分解

csc (x) + csc (x) cot (x) : csc (x) (cot (x) + 1)

csc (x) + csc (x) cot (x)

因式分解出通项

csc (x)

= csc (x) (1 + cot (x))

csc (x) (cot (x) + 1) = 0

分别求解每个部分

csc (x) = 0 or cot (x) + 1 = 0

csc (x) = 0 :

无解

csc (x) = 0

csc (x) \leq - 1 or csc (x) \geq 1

无解

cot (x) + 1 = 0 : x = \frac{3 π}{4} + πn

cot (x) + 1 = 0

将

1

到右边

cot (x) + 1 = 0

两边减去

1

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

化简

cot (x) = - 1

cot (x) = - 1

cot (x) = - 1

的通解

cot (x)

周期表（周期为

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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

合并所有解

x = \frac{3 π}{4} + πn

作图

流行的例子

cot (x) = - \frac{4}{3}

(cos^2(x))/(sin^2(x))=1

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

solvefor x,f=(cos(2x))/(cos(x)-sin(x))

so l v e f or x, f = \frac{cos ( 2 x )}{cos ( x ) - sin ( x )}

cos (2 x) + 5 = 6.25

sin (x) = 4 sin (8)