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受欢迎的三角函数 >

4cos(x)=sqrt(2)+2cos(x)

解答

4 cos (x) = 2 + 2 cos (x)

解答

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

+1

度数

x = 4 5^{\circ} + 36 0^{\circ} n, x = 31 5^{\circ} + 36 0^{\circ} n

求解步骤

4 cos (x) = 2 + 2 cos (x)

用替代法求解

4 cos (x) = 2 + 2 cos (x)

令

: cos (x) = u

4 u = 2 + 2 u

4 u = 2 + 2 u : u = \frac{2}{2}

4 u = 2 + 2 u

将

2 u

para o lado esquerdo

4 u = 2 + 2 u

两边减去

2 u

4 u - 2 u = 2 + 2 u - 2 u

化简

2 u = 2

2 u = 2

两边除以

2

2 u = 2

两边除以

2

\frac{2 u}{2} = \frac{2}{2}

化简

u = \frac{2}{2}

u = \frac{2}{2}

u = cos (x)

代回

cos (x) = \frac{2}{2}

cos (x) = \frac{2}{2}

cos (x) = \frac{2}{2} : x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

cos (x) = \frac{2}{2}

cos (x) = \frac{2}{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{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

合并所有解

x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

作图

流行的例子

4cos(θ)=4sqrt(3)sin(θ)

4 cos (θ) = 43 sin (θ)

14 sin (2 x) + 7 = 0

cos^2(x)+4cos(x)-2=0

cos^{2} (x) + 4 cos (x) - 2 = 0

sec^2(θ)+csc^2(θ)=4

sec^{2} (θ) + csc^{2} (θ) = 4

sin(x)-cos(x)= 1/5

sin (x) - cos (x) = \frac{1}{5}