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受欢迎的三角函数 >

csc(7x+3)=sqrt(2)

解答

csc (7 x + 3) = 2

解答

x = - \frac{3}{7} + \frac{π}{28} + \frac{2 πn}{7}, x = - \frac{3}{7} + \frac{3 π}{28} + \frac{2 πn}{7}

+1

度数

x = - 18.12676 \dots^{\circ} + 51.42857 \dots^{\circ} n, x = - 5.26961 \dots^{\circ} + 51.42857 \dots^{\circ} n

求解步骤

csc (7 x + 3) = 2

csc (7 x + 3) = 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

7 x + 3 = \frac{π}{4} + 2 πn, 7 x + 3 = \frac{3 π}{4} + 2 πn

7 x + 3 = \frac{π}{4} + 2 πn, 7 x + 3 = \frac{3 π}{4} + 2 πn

解

7 x + 3 = \frac{π}{4} + 2 πn : x = - \frac{3}{7} + \frac{π}{28} + \frac{2 πn}{7}

7 x + 3 = \frac{π}{4} + 2 πn

将

3

到右边

7 x + 3 = \frac{π}{4} + 2 πn

两边减去

3

7 x + 3 - 3 = \frac{π}{4} + 2 πn - 3

化简

7 x = \frac{π}{4} + 2 πn - 3

7 x = \frac{π}{4} + 2 πn - 3

两边除以

7

7 x = \frac{π}{4} + 2 πn - 3

两边除以

7

\frac{7 x}{7} = \frac{\frac{π}{4}}{7} + \frac{2 πn}{7} - \frac{3}{7}

化简

\frac{7 x}{7} = \frac{\frac{π}{4}}{7} + \frac{2 πn}{7} - \frac{3}{7}

化简

\frac{7 x}{7} : x

\frac{7 x}{7}

数字相除:

\frac{7}{7} = 1

= x

化简

\frac{\frac{π}{4}}{7} + \frac{2 πn}{7} - \frac{3}{7} : - \frac{3}{7} + \frac{π}{28} + \frac{2 πn}{7}

\frac{\frac{π}{4}}{7} + \frac{2 πn}{7} - \frac{3}{7}

对同类项分组

= - \frac{3}{7} + \frac{2 πn}{7} + \frac{\frac{π}{4}}{7}

\frac{\frac{π}{4}}{7} = \frac{π}{28}

\frac{\frac{π}{4}}{7}

使用分式法则:

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

= \frac{π}{4 \cdot 7}

数字相乘:

4 \cdot 7 = 28

= \frac{π}{28}

= - \frac{3}{7} + \frac{2 πn}{7} + \frac{π}{28}

对同类项分组

= - \frac{3}{7} + \frac{π}{28} + \frac{2 πn}{7}

x = - \frac{3}{7} + \frac{π}{28} + \frac{2 πn}{7}

x = - \frac{3}{7} + \frac{π}{28} + \frac{2 πn}{7}

x = - \frac{3}{7} + \frac{π}{28} + \frac{2 πn}{7}

解

7 x + 3 = \frac{3 π}{4} + 2 πn : x = - \frac{3}{7} + \frac{3 π}{28} + \frac{2 πn}{7}

7 x + 3 = \frac{3 π}{4} + 2 πn

将

3

到右边

7 x + 3 = \frac{3 π}{4} + 2 πn

两边减去

3

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

化简

7 x = \frac{3 π}{4} + 2 πn - 3

7 x = \frac{3 π}{4} + 2 πn - 3

两边除以

7

7 x = \frac{3 π}{4} + 2 πn - 3

两边除以

7

\frac{7 x}{7} = \frac{\frac{3 π}{4}}{7} + \frac{2 πn}{7} - \frac{3}{7}

化简

\frac{7 x}{7} = \frac{\frac{3 π}{4}}{7} + \frac{2 πn}{7} - \frac{3}{7}

化简

\frac{7 x}{7} : x

\frac{7 x}{7}

数字相除:

\frac{7}{7} = 1

= x

化简

\frac{\frac{3 π}{4}}{7} + \frac{2 πn}{7} - \frac{3}{7} : - \frac{3}{7} + \frac{3 π}{28} + \frac{2 πn}{7}

\frac{\frac{3 π}{4}}{7} + \frac{2 πn}{7} - \frac{3}{7}

对同类项分组

= - \frac{3}{7} + \frac{2 πn}{7} + \frac{\frac{3 π}{4}}{7}

\frac{\frac{3 π}{4}}{7} = \frac{3 π}{28}

\frac{\frac{3 π}{4}}{7}

使用分式法则:

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

= \frac{3 π}{4 \cdot 7}

数字相乘:

4 \cdot 7 = 28

= \frac{3 π}{28}

= - \frac{3}{7} + \frac{2 πn}{7} + \frac{3 π}{28}

对同类项分组

= - \frac{3}{7} + \frac{3 π}{28} + \frac{2 πn}{7}

x = - \frac{3}{7} + \frac{3 π}{28} + \frac{2 πn}{7}

x = - \frac{3}{7} + \frac{3 π}{28} + \frac{2 πn}{7}

x = - \frac{3}{7} + \frac{3 π}{28} + \frac{2 πn}{7}

x = - \frac{3}{7} + \frac{π}{28} + \frac{2 πn}{7}, x = - \frac{3}{7} + \frac{3 π}{28} + \frac{2 πn}{7}

作图

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