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受欢迎的三角函数 >

15cos(x)+8=-cos(x)

解答

15 cos (x) + 8 = - 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

15 cos (x) + 8 = - cos (x)

用替代法求解

15 cos (x) + 8 = - cos (x)

令

: cos (x) = u

15 u + 8 = - u

15 u + 8 = - u : u = - \frac{1}{2}

15 u + 8 = - u

将

8

到右边

15 u + 8 = - u

两边减去

8

15 u + 8 - 8 = - u - 8

化简

15 u = - u - 8

15 u = - u - 8

将

u

para o lado esquerdo

15 u = - u - 8

两边加上

u

15 u + u = - u - 8 + u

化简

16 u = - 8

16 u = - 8

两边除以

16

16 u = - 8

两边除以

16

\frac{16 u}{16} = \frac{- 8}{16}

化简

\frac{16 u}{16} = \frac{- 8}{16}

化简

\frac{16 u}{16} : u

\frac{16 u}{16}

数字相除:

\frac{16}{16} = 1

= u

化简

\frac{- 8}{16} : - \frac{1}{2}

\frac{- 8}{16}

使用分式法则:

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

= - \frac{8}{16}

约分:

8

= - \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

cos(2x+pi/6)=(sqrt(3))/2

cos (2 x + \frac{π}{6}) = \frac{3}{2}

4 sin (x) - 2 = 0

cos (2 x) = 3

tan (3 x) + 1 = 0

2cos(x)=4cos(x)sin^2(x)

2 cos (x) = 4 cos (x) sin^{2} (x)