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受欢迎的三角函数 >

2+2cos(t)=6cos(t)

解答

2 + 2 cos (t) = 6 cos (t)

解答

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

+1

度数

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

求解步骤

2 + 2 cos (t) = 6 cos (t)

用替代法求解

2 + 2 cos (t) = 6 cos (t)

令

: cos (t) = u

2 + 2 u = 6 u

2 + 2 u = 6 u : u = \frac{1}{2}

2 + 2 u = 6 u

将

2

到右边

2 + 2 u = 6 u

两边减去

2

2 + 2 u - 2 = 6 u - 2

化简

2 u = 6 u - 2

2 u = 6 u - 2

将

6 u

para o lado esquerdo

2 u = 6 u - 2

两边减去

6 u

2 u - 6 u = 6 u - 2 - 6 u

化简

- 4 u = - 2

- 4 u = - 2

两边除以

- 4

- 4 u = - 2

两边除以

- 4

\frac{- 4 u}{- 4} = \frac{- 2}{- 4}

化简

\frac{- 4 u}{- 4} = \frac{- 2}{- 4}

化简

\frac{- 4 u}{- 4} : u

\frac{- 4 u}{- 4}

使用分式法则:

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

= \frac{4 u}{4}

数字相除:

\frac{4}{4} = 1

= u

化简

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

\frac{- 2}{- 4}

使用分式法则:

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

= \frac{2}{4}

约分:

2

= \frac{1}{2}

u = \frac{1}{2}

u = \frac{1}{2}

u = \frac{1}{2}

u = cos (t)

代回

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

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

cos (t) = \frac{1}{2} : t = \frac{π}{3} + 2 πn, t = \frac{5 π}{3} + 2 πn

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

cos (t) = \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}

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

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

合并所有解

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

作图

流行的例子

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sin(((60))/7)=sin(((81))/a)

sin (\frac{( 60 )}{7}) = sin (\frac{( 81 )}{a})

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