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受欢迎的三角函数 >

4cos(x)=3+8cos(x)

解答

4 cos (x) = 3 + 8 cos (x)

解答

x = 2.41885 \dots + 2 πn, x = - 2.41885 \dots + 2 πn

+1

度数

x = 138.59037 \dots^{\circ} + 36 0^{\circ} n, x = - 138.59037 \dots^{\circ} + 36 0^{\circ} n

求解步骤

4 cos (x) = 3 + 8 cos (x)

用替代法求解

4 cos (x) = 3 + 8 cos (x)

令

: cos (x) = u

4 u = 3 + 8 u

4 u = 3 + 8 u : u = - \frac{3}{4}

4 u = 3 + 8 u

将

8 u

para o lado esquerdo

4 u = 3 + 8 u

两边减去

8 u

4 u - 8 u = 3 + 8 u - 8 u

化简

- 4 u = 3

- 4 u = 3

两边除以

- 4

- 4 u = 3

两边除以

- 4

\frac{- 4 u}{- 4} = \frac{3}{- 4}

化简

u = - \frac{3}{4}

u = - \frac{3}{4}

u = cos (x)

代回

cos (x) = - \frac{3}{4}

cos (x) = - \frac{3}{4}

cos (x) = - \frac{3}{4} : x = arccos (- \frac{3}{4}) + 2 πn, x = - arccos (- \frac{3}{4}) + 2 πn

cos (x) = - \frac{3}{4}

使用反三角函数性质

cos (x) = - \frac{3}{4}

cos (x) = - \frac{3}{4}

的通解

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

x = arccos (- \frac{3}{4}) + 2 πn, x = - arccos (- \frac{3}{4}) + 2 πn

x = arccos (- \frac{3}{4}) + 2 πn, x = - arccos (- \frac{3}{4}) + 2 πn

合并所有解

x = arccos (- \frac{3}{4}) + 2 πn, x = - arccos (- \frac{3}{4}) + 2 πn

以小数形式表示解

x = 2.41885 \dots + 2 πn, x = - 2.41885 \dots + 2 πn

作图

流行的例子

sin^2(θ)-3sin(θ)=0

sin^{2} (θ) - 3 sin (θ) = 0

cos^{2} (x) = \frac{1}{5}

-3cos(2θ)+5=7sin(θ)+5

- 3 cos (2 θ) + 5 = 7 sin (θ) + 5

3+3cos(x)=2sin^2(x)

3 + 3 cos (x) = 2 sin^{2} (x)

cos(θ)=-sin(θ)

cos (θ) = - sin (θ)