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

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

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

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

4788 cos (b) + 5413 = 1849

Move

5413

to the right side

4788 cos (b) = - 3564

Divide both sides by

4788

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

Apply trig inverse properties

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

cos^{2} (x) - 4 cos (x) + 4 = 0

t, x - 4 = sec^{2} (t)

csc (θ) = \frac{34}{3}, cos (θ) > 0

2 sin^{2} (θ) - 3 sin (θ) cos (θ) + cos^{2} (θ) = 0

sin^{2} (x) + 4 cos^{2} (x) = 1

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