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受欢迎的三角函数 >

cos^2(x/2)=1

解答

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

解答

x = 4 πn, x = 2 π + 4 πn

+1

度数

x = 0^{\circ} + 72 0^{\circ} n, x = 36 0^{\circ} + 72 0^{\circ} n

求解步骤

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

用替代法求解

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

令

: cos (\frac{x}{2}) = u

u^{2} = 1

u^{2} = 1 : u = 1, u = - 1

u^{2} = 1

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = 1, u = - 1

1 = 1

1

使用法则

1 = 1

= 1

- 1 = - 1

- 1

使用法则

1 = 1

= - 1

u = 1, u = - 1

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

代回

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

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

cos (\frac{x}{2}) = 1 : x = 4 πn

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

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

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}

\frac{x}{2} = 0 + 2 πn

\frac{x}{2} = 0 + 2 πn

解

\frac{x}{2} = 0 + 2 πn : x = 4 πn

\frac{x}{2} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{x}{2} = 2 πn

在两边乘以

2

\frac{x}{2} = 2 πn

在两边乘以

2

\frac{2 x}{2} = 2 \cdot 2 πn

化简

x = 4 πn

x = 4 πn

x = 4 πn

cos (\frac{x}{2}) = - 1 : x = 2 π + 4 πn

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

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

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}

\frac{x}{2} = π + 2 πn

\frac{x}{2} = π + 2 πn

解

\frac{x}{2} = π + 2 πn : x = 2 π + 4 πn

\frac{x}{2} = π + 2 πn

在两边乘以

2

\frac{x}{2} = π + 2 πn

在两边乘以

2

\frac{2 x}{2} = 2 π + 2 \cdot 2 πn

化简

x = 2 π + 4 πn

x = 2 π + 4 πn

x = 2 π + 4 πn

合并所有解

x = 4 πn, x = 2 π + 4 πn

作图

流行的例子

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