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受欢迎的三角函数 >

7cos(x)+9=-2cos(x)

解答

7 cos (x) + 9 = - 2 cos (x)

解答

x = π + 2 πn

+1

度数

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

求解步骤

7 cos (x) + 9 = - 2 cos (x)

用替代法求解

7 cos (x) + 9 = - 2 cos (x)

令

: cos (x) = u

7 u + 9 = - 2 u

7 u + 9 = - 2 u : u = - 1

7 u + 9 = - 2 u

将

9

到右边

7 u + 9 = - 2 u

两边减去

9

7 u + 9 - 9 = - 2 u - 9

化简

7 u = - 2 u - 9

7 u = - 2 u - 9

将

2 u

para o lado esquerdo

7 u = - 2 u - 9

两边加上

2 u

7 u + 2 u = - 2 u - 9 + 2 u

化简

9 u = - 9

9 u = - 9

两边除以

9

9 u = - 9

两边除以

9

\frac{9 u}{9} = \frac{- 9}{9}

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

sqrt(5)cot(x/2)=sqrt(5)

5 cot (\frac{x}{2}) = 5

tan (θ) = \frac{8}{7}

sqrt(1-cos(x))=sin(x)

1 - cos (x) = sin (x)

tan (x) = \frac{15}{8}

tan^2(x)+3sec(x)+3=0

tan^{2} (x) + 3 sec (x) + 3 = 0