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受欢迎的三角函数 >

1-cos(x)= 1/2

解答

1 - cos (x) = \frac{1}{2}

解答

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

+1

度数

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

求解步骤

1 - cos (x) = \frac{1}{2}

将

1

到右边

1 - cos (x) = \frac{1}{2}

两边减去

1

1 - cos (x) - 1 = \frac{1}{2} - 1

化简

1 - cos (x) - 1 = \frac{1}{2} - 1

化简

1 - cos (x) - 1 : - cos (x)

1 - cos (x) - 1

同类项相加:

1 - 1 = 0

= - cos (x)

化简

\frac{1}{2} - 1 : - \frac{1}{2}

\frac{1}{2} - 1

将项转换为分式:

1 = \frac{1 \cdot 2}{2}

= - \frac{1 \cdot 2}{2} + \frac{1}{2}

因为分母相等，所以合并分式:

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

= \frac{- 1 \cdot 2 + 1}{2}

- 1 \cdot 2 + 1 = - 1

- 1 \cdot 2 + 1

数字相乘:

1 \cdot 2 = 2

= - 2 + 1

数字相加/相减:

- 2 + 1 = - 1

= - 1

= \frac{- 1}{2}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1}{2}

- cos (x) = - \frac{1}{2}

- cos (x) = - \frac{1}{2}

- cos (x) = - \frac{1}{2}

两边除以

- 1

- cos (x) = - \frac{1}{2}

两边除以

- 1

\frac{- cos ( x )}{- 1} = \frac{- \frac{1}{2}}{- 1}

化简

\frac{- cos ( x )}{- 1} = \frac{- \frac{1}{2}}{- 1}

化简

\frac{- cos ( x )}{- 1} : cos (x)

\frac{- cos ( x )}{- 1}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

= \frac{cos ( x )}{1}

使用法则

\frac{a}{1} = a

= cos (x)

化简

\frac{- \frac{1}{2}}{- 1} : \frac{1}{2}

\frac{- \frac{1}{2}}{- 1}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

= \frac{\frac{1}{2}}{1}

使用分式法则:

\frac{a}{1} = a

= \frac{1}{2}

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

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

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

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

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}

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

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

作图

流行的例子

4cos^3(x)=4cos(x)

4 cos^{3} (x) = 4 cos (x)

sec (x) = \frac{5}{4}

sin(x)tan(x)=-9tan(x)

sin (x) tan (x) = - 9 tan (x)

cos(x)-cos(3x)=0

cos (x) - cos (3 x) = 0

5cos(x)tan(x)+3tan(x)=0

5 cos (x) tan (x) + 3 tan (x) = 0