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受欢迎的三角函数 >

8^2=14^2+19^2-2(14)(19)cos(C)

解答

8^{2} = 1 4^{2} + 1 9^{2} - 2 (14) (19) cos (C)

解答

C = 0.38528 \dots + 2 πn, C = 2 π - 0.38528 \dots + 2 πn

+1

度数

C = 22.07514 \dots^{\circ} + 36 0^{\circ} n, C = 337.92485 \dots^{\circ} + 36 0^{\circ} n

求解步骤

8^{2} = 1 4^{2} + 1 9^{2} - 2 (14) (19) cos (C)

交换两边

1 4^{2} + 1 9^{2} - 2 \cdot 14 \cdot 19 cos (C) = 8^{2}

数字相乘:

2 \cdot 14 \cdot 19 = 532

1 4^{2} + 1 9^{2} - 532 cos (C) = 8^{2}

1 4^{2} = 196

196 + 1 9^{2} - 532 cos (C) = 8^{2}

1 9^{2} = 361

196 + 361 - 532 cos (C) = 8^{2}

数字相加:

196 + 361 = 557

- 532 cos (C) + 557 = 8^{2}

8^{2} = 64

- 532 cos (C) + 557 = 64

将

557

到右边

- 532 cos (C) + 557 = 64

两边减去

557

- 532 cos (C) + 557 - 557 = 64 - 557

化简

- 532 cos (C) = - 493

- 532 cos (C) = - 493

两边除以

- 532

- 532 cos (C) = - 493

两边除以

- 532

\frac{- 532 cos ( C )}{- 532} = \frac{- 493}{- 532}

化简

cos (C) = \frac{493}{532}

cos (C) = \frac{493}{532}

使用反三角函数性质

cos (C) = \frac{493}{532}

cos (C) = \frac{493}{532}

的通解

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

C = arccos (\frac{493}{532}) + 2 πn, C = 2 π - arccos (\frac{493}{532}) + 2 πn

C = arccos (\frac{493}{532}) + 2 πn, C = 2 π - arccos (\frac{493}{532}) + 2 πn

以小数形式表示解

C = 0.38528 \dots + 2 πn, C = 2 π - 0.38528 \dots + 2 πn

作图

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