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受欢迎的三角函数 >

(csc(x)+2)(csc(x)-sqrt(2))=0,0<= x<= 2pi

解答

(csc (x) + 2) (csc (x) - 2) = 0, 0 \leq x \leq 2 π

解答

x = \frac{7 π}{6}, x = \frac{11 π}{6}, x = \frac{π}{4}, x = \frac{3 π}{4}

+1

度数

x = 21 0^{\circ}, x = 33 0^{\circ}, x = 4 5^{\circ}, x = 13 5^{\circ}

求解步骤

(csc (x) + 2) (csc (x) - 2) = 0, 0 \leq x \leq 2 π

分别求解每个部分

csc (x) + 2 = 0 or csc (x) - 2 = 0

csc (x) + 2 = 0, 0 \leq x \leq 2 π : x = \frac{7 π}{6}, x = \frac{11 π}{6}

csc (x) + 2 = 0, 0 \leq x \leq 2 π

将

2

到右边

csc (x) + 2 = 0

两边减去

2

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

化简

csc (x) = - 2

csc (x) = - 2

csc (x) = - 2

的通解

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

在

0 \leq x \leq 2 π

范围内的解

x = \frac{7 π}{6}, x = \frac{11 π}{6}

csc (x) - 2 = 0, 0 \leq x \leq 2 π : x = \frac{π}{4}, x = \frac{3 π}{4}

csc (x) - 2 = 0, 0 \leq x \leq 2 π

将

2

到右边

csc (x) - 2 = 0

两边加上

2

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

化简

csc (x) = 2

csc (x) = 2

csc (x) = 2

的通解

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

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

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

在

0 \leq x \leq 2 π

范围内的解

x = \frac{π}{4}, x = \frac{3 π}{4}

合并所有解

x = \frac{7 π}{6}, x = \frac{11 π}{6}, x = \frac{π}{4}, x = \frac{3 π}{4}

作图

流行的例子

(51)/(sin(93))=(43)/(sin(C))