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受欢迎的三角函数 >

0=cos(5θ)

解答

0 = cos (5 θ)

解答

θ = \frac{π}{10} + \frac{2 πn}{5}, θ = \frac{3 π}{10} + \frac{2 πn}{5}

+1

度数

θ = 1 8^{\circ} + 7 2^{\circ} n, θ = 5 4^{\circ} + 7 2^{\circ} n

求解步骤

0 = cos (5 θ)

交换两边

cos (5 θ) = 0

cos (5 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}

5 θ = \frac{π}{2} + 2 πn, 5 θ = \frac{3 π}{2} + 2 πn

5 θ = \frac{π}{2} + 2 πn, 5 θ = \frac{3 π}{2} + 2 πn

解

5 θ = \frac{π}{2} + 2 πn : θ = \frac{π}{10} + \frac{2 πn}{5}

5 θ = \frac{π}{2} + 2 πn

两边除以

5

5 θ = \frac{π}{2} + 2 πn

两边除以

5

\frac{5 θ}{5} = \frac{\frac{π}{2}}{5} + \frac{2 πn}{5}

化简

\frac{5 θ}{5} = \frac{\frac{π}{2}}{5} + \frac{2 πn}{5}

化简

\frac{5 θ}{5} : θ

\frac{5 θ}{5}

数字相除:

\frac{5}{5} = 1

= θ

化简

\frac{\frac{π}{2}}{5} + \frac{2 πn}{5} : \frac{π}{10} + \frac{2 πn}{5}

\frac{\frac{π}{2}}{5} + \frac{2 πn}{5}

\frac{\frac{π}{2}}{5} = \frac{π}{10}

\frac{\frac{π}{2}}{5}

使用分式法则:

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

= \frac{π}{2 \cdot 5}

数字相乘:

2 \cdot 5 = 10

= \frac{π}{10}

= \frac{π}{10} + \frac{2 πn}{5}

θ = \frac{π}{10} + \frac{2 πn}{5}

θ = \frac{π}{10} + \frac{2 πn}{5}

θ = \frac{π}{10} + \frac{2 πn}{5}

解

5 θ = \frac{3 π}{2} + 2 πn : θ = \frac{3 π}{10} + \frac{2 πn}{5}

5 θ = \frac{3 π}{2} + 2 πn

两边除以

5

5 θ = \frac{3 π}{2} + 2 πn

两边除以

5

\frac{5 θ}{5} = \frac{\frac{3 π}{2}}{5} + \frac{2 πn}{5}

化简

\frac{5 θ}{5} = \frac{\frac{3 π}{2}}{5} + \frac{2 πn}{5}

化简

\frac{5 θ}{5} : θ

\frac{5 θ}{5}

数字相除:

\frac{5}{5} = 1

= θ

化简

\frac{\frac{3 π}{2}}{5} + \frac{2 πn}{5} : \frac{3 π}{10} + \frac{2 πn}{5}

\frac{\frac{3 π}{2}}{5} + \frac{2 πn}{5}

\frac{\frac{3 π}{2}}{5} = \frac{3 π}{10}

\frac{\frac{3 π}{2}}{5}

使用分式法则:

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

= \frac{3 π}{2 \cdot 5}

数字相乘:

2 \cdot 5 = 10

= \frac{3 π}{10}

= \frac{3 π}{10} + \frac{2 πn}{5}

θ = \frac{3 π}{10} + \frac{2 πn}{5}

θ = \frac{3 π}{10} + \frac{2 πn}{5}

θ = \frac{3 π}{10} + \frac{2 πn}{5}

θ = \frac{π}{10} + \frac{2 πn}{5}, θ = \frac{3 π}{10} + \frac{2 πn}{5}

作图

流行的例子

cos (x) = 0.63

cos (x) = 0.58

cos (x) = 0.41

cos (x) = 0.42

cos (x) = 0.36