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受欢迎的三角函数 >

3cos(7θ)=0

解答

3 cos (7 θ) = 0

解答

θ = \frac{π}{14} + \frac{2 πn}{7}, θ = \frac{3 π}{14} + \frac{2 πn}{7}

+1

度数

θ = 12.85714 \dots^{\circ} + 51.42857 \dots^{\circ} n, θ = 38.57142 \dots^{\circ} + 51.42857 \dots^{\circ} n

求解步骤

3 cos (7 θ) = 0

两边除以

3

3 cos (7 θ) = 0

两边除以

3

\frac{3 cos ( 7 θ )}{3} = \frac{0}{3}

化简

cos (7 θ) = 0

cos (7 θ) = 0

cos (7 θ) = 0

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}

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

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

解

7 θ = \frac{π}{2} + 2 πn : θ = \frac{π}{14} + \frac{2 πn}{7}

7 θ = \frac{π}{2} + 2 πn

两边除以

7

7 θ = \frac{π}{2} + 2 πn

两边除以

7

\frac{7 θ}{7} = \frac{\frac{π}{2}}{7} + \frac{2 πn}{7}

化简

\frac{7 θ}{7} = \frac{\frac{π}{2}}{7} + \frac{2 πn}{7}

化简

\frac{7 θ}{7} : θ

\frac{7 θ}{7}

数字相除:

\frac{7}{7} = 1

= θ

化简

\frac{\frac{π}{2}}{7} + \frac{2 πn}{7} : \frac{π}{14} + \frac{2 πn}{7}

\frac{\frac{π}{2}}{7} + \frac{2 πn}{7}

\frac{\frac{π}{2}}{7} = \frac{π}{14}

\frac{\frac{π}{2}}{7}

使用分式法则:

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

= \frac{π}{2 \cdot 7}

数字相乘:

2 \cdot 7 = 14

= \frac{π}{14}

= \frac{π}{14} + \frac{2 πn}{7}

θ = \frac{π}{14} + \frac{2 πn}{7}

θ = \frac{π}{14} + \frac{2 πn}{7}

θ = \frac{π}{14} + \frac{2 πn}{7}

解

7 θ = \frac{3 π}{2} + 2 πn : θ = \frac{3 π}{14} + \frac{2 πn}{7}

7 θ = \frac{3 π}{2} + 2 πn

两边除以

7

7 θ = \frac{3 π}{2} + 2 πn

两边除以

7

\frac{7 θ}{7} = \frac{\frac{3 π}{2}}{7} + \frac{2 πn}{7}

化简

\frac{7 θ}{7} = \frac{\frac{3 π}{2}}{7} + \frac{2 πn}{7}

化简

\frac{7 θ}{7} : θ

\frac{7 θ}{7}

数字相除:

\frac{7}{7} = 1

= θ

化简

\frac{\frac{3 π}{2}}{7} + \frac{2 πn}{7} : \frac{3 π}{14} + \frac{2 πn}{7}

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

\frac{\frac{3 π}{2}}{7} = \frac{3 π}{14}

\frac{\frac{3 π}{2}}{7}

使用分式法则:

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

= \frac{3 π}{2 \cdot 7}

数字相乘:

2 \cdot 7 = 14

= \frac{3 π}{14}

= \frac{3 π}{14} + \frac{2 πn}{7}

θ = \frac{3 π}{14} + \frac{2 πn}{7}

θ = \frac{3 π}{14} + \frac{2 πn}{7}

θ = \frac{3 π}{14} + \frac{2 πn}{7}

θ = \frac{π}{14} + \frac{2 πn}{7}, θ = \frac{3 π}{14} + \frac{2 πn}{7}

作图

流行的例子

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\frac{( cos ( x ) cot ( x ) )}{( 1 - sin ( x ) ) - 1} = csc (x)

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