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受欢迎的三角函数 >

-2cos(B)+4=cos(B)+6

解答

- 2 cos (B) + 4 = cos (B) + 6

解答

B = 2.30052 \dots + 2 πn, B = - 2.30052 \dots + 2 πn

+1

度数

B = 131.81031 \dots^{\circ} + 36 0^{\circ} n, B = - 131.81031 \dots^{\circ} + 36 0^{\circ} n

求解步骤

- 2 cos (B) + 4 = cos (B) + 6

用替代法求解

- 2 cos (B) + 4 = cos (B) + 6

令

: cos (B) = u

- 2 u + 4 = u + 6

- 2 u + 4 = u + 6 : u = - \frac{2}{3}

- 2 u + 4 = u + 6

将

4

到右边

- 2 u + 4 = u + 6

两边减去

4

- 2 u + 4 - 4 = u + 6 - 4

化简

- 2 u = u + 2

- 2 u = u + 2

将

u

para o lado esquerdo

- 2 u = u + 2

两边减去

u

- 2 u - u = u + 2 - u

化简

- 3 u = 2

- 3 u = 2

两边除以

- 3

- 3 u = 2

两边除以

- 3

\frac{- 3 u}{- 3} = \frac{2}{- 3}

化简

u = - \frac{2}{3}

u = - \frac{2}{3}

u = cos (B)

代回

cos (B) = - \frac{2}{3}

cos (B) = - \frac{2}{3}

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

cos (B) = - \frac{2}{3}

使用反三角函数性质

cos (B) = - \frac{2}{3}

cos (B) = - \frac{2}{3}

的通解

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

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

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

合并所有解

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

以小数形式表示解

B = 2.30052 \dots + 2 πn, B = - 2.30052 \dots + 2 πn

作图

流行的例子

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