What is the general solution for 4.3^2=3.8^2+6.3^2+2(3.8)(6.3)cos(b) ?

The general solution for 4.3^2=3.8^2+6.3^2+2(3.8)(6.3)cos(b) is b=2.41037…+2pin,b=-2.41037…+2pin

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Popular Trigonometry >

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

Solution

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

Solution

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

Degrees

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

Solution steps

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

Switch sides

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

Multiply the numbers:

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}

Add the numbers:

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

Multiply both sides by

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

Refine

4788 cos (b) + 5413 = 1849

4788 cos (b) + 5413 = 1849

Move

5413

to the right side

4788 cos (b) + 5413 = 1849

Subtract

5413

from both sides

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

Simplify

4788 cos (b) = - 3564

4788 cos (b) = - 3564

Divide both sides by

4788

4788 cos (b) = - 3564

Divide both sides by

4788

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

Simplify

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

Simplify

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

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

Divide the numbers:

\frac{4788}{4788} = 1

= cos (b)

Simplify

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

\frac{- 3564}{4788}

Apply the fraction rule:

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

= - \frac{3564}{4788}

Cancel the common factor:

36

= - \frac{99}{133}

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

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

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

Apply trig inverse properties

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

General solutions for

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

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

Show solutions in decimal form

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

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 4.3^2=3.8^2+6.3^2+2(3.8)(6.3)cos(b) ?
The general solution for 4.3^2=3.8^2+6.3^2+2(3.8)(6.3)cos(b) is b=2.41037…+2pin,b=-2.41037…+2pin