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受欢迎的三角函数 >

cos^2(5x)=1

解答

cos^{2} (5 x) = 1

解答

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

+1

度数

x = 0^{\circ} + 7 2^{\circ} n, x = 3 6^{\circ} + 7 2^{\circ} n

求解步骤

cos^{2} (5 x) = 1

用替代法求解

cos^{2} (5 x) = 1

令

: cos (5 x) = 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 (5 x)

代回

cos (5 x) = 1, cos (5 x) = - 1

cos (5 x) = 1, cos (5 x) = - 1

cos (5 x) = 1 : x = \frac{2 πn}{5}

cos (5 x) = 1

cos (5 x) = 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}

5 x = 0 + 2 πn

5 x = 0 + 2 πn

解

5 x = 0 + 2 πn : x = \frac{2 πn}{5}

5 x = 0 + 2 πn

0 + 2 πn = 2 πn

5 x = 2 πn

两边除以

5

5 x = 2 πn

两边除以

5

\frac{5 x}{5} = \frac{2 πn}{5}

化简

x = \frac{2 πn}{5}

x = \frac{2 πn}{5}

x = \frac{2 πn}{5}

cos (5 x) = - 1 : x = \frac{π}{5} + \frac{2 πn}{5}

cos (5 x) = - 1

cos (5 x) = - 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}

5 x = π + 2 πn

5 x = π + 2 πn

解

5 x = π + 2 πn : x = \frac{π}{5} + \frac{2 πn}{5}

5 x = π + 2 πn

两边除以

5

5 x = π + 2 πn

两边除以

5

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

化简

x = \frac{π}{5} + \frac{2 πn}{5}

x = \frac{π}{5} + \frac{2 πn}{5}

x = \frac{π}{5} + \frac{2 πn}{5}

合并所有解

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

作图

流行的例子

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1+cos(x)=sin^2(x)

1 + cos (x) = sin^{2} (x)

tan(x-pi/2)= 1/(sqrt(3))

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