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受欢迎的三角函数 >

-2cos(C)+5=2cos(C)+4

解答

- 2 cos (C) + 5 = 2 cos (C) + 4

解答

C = 1.31811 \dots + 2 πn, C = 2 π - 1.31811 \dots + 2 πn

+1

度数

C = 75.52248 \dots^{\circ} + 36 0^{\circ} n, C = 284.47751 \dots^{\circ} + 36 0^{\circ} n

求解步骤

- 2 cos (C) + 5 = 2 cos (C) + 4

用替代法求解

- 2 cos (C) + 5 = 2 cos (C) + 4

令

: cos (C) = u

- 2 u + 5 = 2 u + 4

- 2 u + 5 = 2 u + 4 : u = \frac{1}{4}

- 2 u + 5 = 2 u + 4

将

5

到右边

- 2 u + 5 = 2 u + 4

两边减去

5

- 2 u + 5 - 5 = 2 u + 4 - 5

化简

- 2 u = 2 u - 1

- 2 u = 2 u - 1

将

2 u

para o lado esquerdo

- 2 u = 2 u - 1

两边减去

2 u

- 2 u - 2 u = 2 u - 1 - 2 u

化简

- 4 u = - 1

- 4 u = - 1

两边除以

- 4

- 4 u = - 1

两边除以

- 4

\frac{- 4 u}{- 4} = \frac{- 1}{- 4}

化简

u = \frac{1}{4}

u = \frac{1}{4}

u = cos (C)

代回

cos (C) = \frac{1}{4}

cos (C) = \frac{1}{4}

cos (C) = \frac{1}{4} : C = arccos (\frac{1}{4}) + 2 πn, C = 2 π - arccos (\frac{1}{4}) + 2 πn

cos (C) = \frac{1}{4}

使用反三角函数性质

cos (C) = \frac{1}{4}

cos (C) = \frac{1}{4}

的通解

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

C = arccos (\frac{1}{4}) + 2 πn, C = 2 π - arccos (\frac{1}{4}) + 2 πn

C = arccos (\frac{1}{4}) + 2 πn, C = 2 π - arccos (\frac{1}{4}) + 2 πn

合并所有解

C = arccos (\frac{1}{4}) + 2 πn, C = 2 π - arccos (\frac{1}{4}) + 2 πn

以小数形式表示解

C = 1.31811 \dots + 2 πn, C = 2 π - 1.31811 \dots + 2 πn

作图

流行的例子

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2 csc^{2} (x) + cot^{2} (x) - 3 = 0

tan (x) = 0.095

sin^2(x)cos^2(x)=1

sin^{2} (x) cos^{2} (x) = 1

-1=-4sec(x)-sec^2(x)-5

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