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受欢迎的三角函数 >

cos(x)-1=2cos(x)

解答

cos (x) - 1 = 2 cos (x)

解答

x = π + 2 πn

+1

度数

x = 18 0^{\circ} + 36 0^{\circ} n

求解步骤

cos (x) - 1 = 2 cos (x)

用替代法求解

cos (x) - 1 = 2 cos (x)

令

: cos (x) = u

u - 1 = 2 u

u - 1 = 2 u : u = - 1

u - 1 = 2 u

将

1

到右边

u - 1 = 2 u

两边加上

1

u - 1 + 1 = 2 u + 1

化简

u = 2 u + 1

u = 2 u + 1

将

2 u

para o lado esquerdo

u = 2 u + 1

两边减去

2 u

u - 2 u = 2 u + 1 - 2 u

化简

- u = 1

- u = 1

两边除以

- 1

- u = 1

两边除以

- 1

\frac{- u}{- 1} = \frac{1}{- 1}

化简

u = - 1

u = - 1

u = cos (x)

代回

cos (x) = - 1

cos (x) = - 1

cos (x) = - 1 : x = π + 2 πn

cos (x) = - 1

cos (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}

x = π + 2 πn

x = π + 2 πn

合并所有解

x = π + 2 πn

作图

流行的例子

cos(5x)=-1,0<= x<2pi

cos (5 x) = - 1, 0 \leq x < 2 π

sinh (x) = - 1

3cos^2(x)+2sin(x)-3=0

3 cos^{2} (x) + 2 sin (x) - 3 = 0

cos (c) = \frac{15}{17}

sin (θ) = 0.3907