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受欢迎的三角函数 >

4.3^2=3.8^2+6.3^2+2(3.8)(6.3)cos(b)

解答

4. 3^{2} = 3. 8^{2} + 6. 3^{2} + 2 (3.8) (6.3) cos (b)

解答

b = 2.41037 \dots + 2 πn, b = - 2.41037 \dots + 2 πn

+1

度数

b = 138.10423 \dots^{\circ} + 36 0^{\circ} n, b = - 138.10423 \dots^{\circ} + 36 0^{\circ} n

求解步骤

4. 3^{2} = 3. 8^{2} + 6. 3^{2} + 2 (3.8) (6.3) cos (b)

交换两边

3. 8^{2} + 6. 3^{2} + 2 \cdot 3.8 \cdot 6.3 cos (b) = 4. 3^{2}

数字相乘:

2 \cdot 3.8 \cdot 6.3 = 47.88

3. 8^{2} + 6. 3^{2} + 47.88 cos (b) = 4. 3^{2}

3. 8^{2} = 14.44

14.44 + 6. 3^{2} + 47.88 cos (b) = 4. 3^{2}

6. 3^{2} = 39.69

14.44 + 39.69 + 47.88 cos (b) = 4. 3^{2}

数字相加:

14.44 + 39.69 = 54.13

47.88 cos (b) + 54.13 = 4. 3^{2}

4. 3^{2} = 18.49

47.88 cos (b) + 54.13 = 18.49

在两边乘以

100

47.88 cos (b) + 54.13 = 18.49

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

47.88 cos (b) \cdot 100 + 54.13 \cdot 100 = 18.49 \cdot 100

整理后得

4788 cos (b) + 5413 = 1849

4788 cos (b) + 5413 = 1849

将

5413

到右边

4788 cos (b) + 5413 = 1849

两边减去

5413

4788 cos (b) + 5413 - 5413 = 1849 - 5413

化简

4788 cos (b) = - 3564

4788 cos (b) = - 3564

两边除以

4788

4788 cos (b) = - 3564

两边除以

4788

\frac{4788 cos ( b )}{4788} = \frac{- 3564}{4788}

化简

\frac{4788 cos ( b )}{4788} = \frac{- 3564}{4788}

化简

\frac{4788 cos ( b )}{4788} : cos (b)

\frac{4788 cos ( b )}{4788}

数字相除:

\frac{4788}{4788} = 1

= cos (b)

化简

\frac{- 3564}{4788} : - \frac{99}{133}

\frac{- 3564}{4788}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{3564}{4788}

约分:

36

= - \frac{99}{133}

cos (b) = - \frac{99}{133}

cos (b) = - \frac{99}{133}

cos (b) = - \frac{99}{133}

使用反三角函数性质

cos (b) = - \frac{99}{133}

cos (b) = - \frac{99}{133}

的通解

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

b = arccos (- \frac{99}{133}) + 2 πn, b = - arccos (- \frac{99}{133}) + 2 πn

b = arccos (- \frac{99}{133}) + 2 πn, b = - arccos (- \frac{99}{133}) + 2 πn

以小数形式表示解

b = 2.41037 \dots + 2 πn, b = - 2.41037 \dots + 2 πn

作图

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