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受欢迎的三角函数 >

7cos(x)+4=-cos(x)

解答

7 cos (x) + 4 = - cos (x)

解答

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

+1

度数

x = 12 0^{\circ} + 36 0^{\circ} n, x = 24 0^{\circ} + 36 0^{\circ} n

求解步骤

7 cos (x) + 4 = - cos (x)

用替代法求解

7 cos (x) + 4 = - cos (x)

令

: cos (x) = u

7 u + 4 = - u

7 u + 4 = - u : u = - \frac{1}{2}

7 u + 4 = - u

将

4

到右边

7 u + 4 = - u

两边减去

4

7 u + 4 - 4 = - u - 4

化简

7 u = - u - 4

7 u = - u - 4

将

u

para o lado esquerdo

7 u = - u - 4

两边加上

u

7 u + u = - u - 4 + u

化简

8 u = - 4

8 u = - 4

两边除以

8

8 u = - 4

两边除以

8

\frac{8 u}{8} = \frac{- 4}{8}

化简

\frac{8 u}{8} = \frac{- 4}{8}

化简

\frac{8 u}{8} : u

\frac{8 u}{8}

数字相除:

\frac{8}{8} = 1

= u

化简

\frac{- 4}{8} : - \frac{1}{2}

\frac{- 4}{8}

使用分式法则:

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

= - \frac{4}{8}

约分:

4

= - \frac{1}{2}

u = - \frac{1}{2}

u = - \frac{1}{2}

u = - \frac{1}{2}

u = cos (x)

代回

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

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

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

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{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

合并所有解

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

作图

流行的例子

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cos^{2} (θ) + cos (θ) = sin^{2} (θ)

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