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受欢迎的三角函数 >

5cos(x)+2=cos(x)

解答

5 cos (x) + 2 = 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

5 cos (x) + 2 = cos (x)

用替代法求解

5 cos (x) + 2 = cos (x)

令

: cos (x) = u

5 u + 2 = u

5 u + 2 = u : u = - \frac{1}{2}

5 u + 2 = u

将

2

到右边

5 u + 2 = u

两边减去

2

5 u + 2 - 2 = u - 2

化简

5 u = u - 2

5 u = u - 2

将

u

para o lado esquerdo

5 u = u - 2

两边减去

u

5 u - u = u - 2 - 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}

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 (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

sec(x)=-5,pi<x<(3pi)/2

sec (x) = - 5, π < x < \frac{3 π}{2}

sin (\frac{θ}{2}) = \frac{3}{5}

2sin^3(t)+sin^2(t)-2sin(t)-1=0

2 sin^{3} (t) + sin^{2} (t) - 2 sin (t) - 1 = 0

sin(x)= 1/5 ,cos(x)>0

sin (x) = \frac{1}{5}, cos (x) > 0

6 cos (x) = 3