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受欢迎的三角函数 >

4cos(x)+6=5(cos(x)+1)

解答

4 cos (x) + 6 = 5 (cos (x) + 1)

解答

x = 2 πn

+1

度数

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

求解步骤

4 cos (x) + 6 = 5 (cos (x) + 1)

用替代法求解

4 cos (x) + 6 = 5 (cos (x) + 1)

令

: cos (x) = u

4 u + 6 = 5 (u + 1)

4 u + 6 = 5 (u + 1) : u = 1

4 u + 6 = 5 (u + 1)

展开

5 (u + 1) : 5 u + 5

5 (u + 1)

使用分配律:

a (b + c) = ab + a c

a = 5, b = u, c = 1

= 5 u + 5 \cdot 1

数字相乘:

5 \cdot 1 = 5

= 5 u + 5

4 u + 6 = 5 u + 5

将

6

到右边

4 u + 6 = 5 u + 5

两边减去

6

4 u + 6 - 6 = 5 u + 5 - 6

化简

4 u = 5 u - 1

4 u = 5 u - 1

将

5 u

para o lado esquerdo

4 u = 5 u - 1

两边减去

5 u

4 u - 5 u = 5 u - 1 - 5 u

化简

- u = - 1

- u = - 1

两边除以

- 1

- u = - 1

两边除以

- 1

\frac{- u}{- 1} = \frac{- 1}{- 1}

化简

u = 1

u = 1

u = cos (x)

代回

cos (x) = 1

cos (x) = 1

cos (x) = 1 : x = 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 = 0 + 2 πn

x = 0 + 2 πn

解

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

合并所有解

x = 2 πn

作图

流行的例子

cos (x) = 0.8736

2sin(x)cos^2(x)-sin(x)=0

2 sin (x) cos^{2} (x) - sin (x) = 0

tan(x)= 1/(sec(x))

tan (x) = \frac{1}{sec ( x )}

4cos(x)+3sin(x)=5

4 cos (x) + 3 sin (x) = 5

tan^2(θ)-sec^2(θ)=cos(-θ)

tan^{2} (θ) - sec^{2} (θ) = cos (- θ)