What is the general solution for 4.58^2=3.3^2+3.3^2-2(3.3)(3.3)cos(x) ?

The general solution for 4.58^2=3.3^2+3.3^2-2(3.3)(3.3)cos(x) is x=1.53389…+2pin,x=2pi-1.53389…+2pin

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4.58^2=3.3^2+3.3^2-2(3.3)(3.3)cos(x)

4.5 8^{2} = 3. 3^{2} + 3. 3^{2} - 2 (3.3) (3.3) cos (x)

x = 1.53389 \dots + 2 πn, x = 2 π - 1.53389 \dots + 2 πn

Degrees

x = 87.88552 \dots^{\circ} + 36 0^{\circ} n, x = 272.11447 \dots^{\circ} + 36 0^{\circ} n

Solution steps

4.5 8^{2} = 3. 3^{2} + 3. 3^{2} - 2 (3.3) (3.3) cos (x)

Switch sides

3. 3^{2} + 3. 3^{2} - 2 \cdot 3.3 \cdot 3.3 cos (x) = 4.5 8^{2}

Simplify

3. 3^{2} + 3. 3^{2} - 2 \cdot 3.3 \cdot 3.3 cos (x) : 21.78 - 21.78 cos (x)

3. 3^{2} + 3. 3^{2} - 2 \cdot 3.3 \cdot 3.3 cos (x)

Add similar elements:

3. 3^{2} + 3. 3^{2} = 2 \cdot 3. 3^{2}

= 2 \cdot 3. 3^{2} - 2 \cdot 3.3 \cdot 3.3 cos (x)

Multiply the numbers:

2 \cdot 3.3 \cdot 3.3 = 21.78

= 2 \cdot 3. 3^{2} - 21.78 cos (x)

2 \cdot 3. 3^{2} = 21.78

2 \cdot 3. 3^{2}

3. 3^{2} = 10.89

= 2 \cdot 10.89

Multiply the numbers:

2 \cdot 10.89 = 21.78

= 21.78

= 21.78 - 21.78 cos (x)

Simplify

4.5 8^{2} : 20.9764

4.5 8^{2}

4.5 8^{2} = 20.9764

= 20.9764

21.78 - 21.78 cos (x) = 20.9764

Move

21.78

to the right side

21.78 - 21.78 cos (x) = 20.9764

Subtract

21.78

from both sides

21.78 - 21.78 cos (x) - 21.78 = 20.9764 - 21.78

Simplify

- 21.78 cos (x) = - 0.8036

- 21.78 cos (x) = - 0.8036

Divide both sides by

- 21.78

- 21.78 cos (x) = - 0.8036

Divide both sides by

- 21.78

\frac{- 21.78 cos ( x )}{- 21.78} = \frac{- 0.8036}{- 21.78}

Simplify

cos (x) = \frac{0.8036}{21.78}

cos (x) = \frac{0.8036}{21.78}

Apply trig inverse properties

cos (x) = \frac{0.8036}{21.78}

General solutions for

cos (x) = \frac{0.8036}{21.78}

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

x = arccos (\frac{0.8036}{21.78}) + 2 πn, x = 2 π - arccos (\frac{0.8036}{21.78}) + 2 πn

x = arccos (\frac{0.8036}{21.78}) + 2 πn, x = 2 π - arccos (\frac{0.8036}{21.78}) + 2 πn

Show solutions in decimal form

x = 1.53389 \dots + 2 πn, x = 2 π - 1.53389 \dots + 2 πn

What is the general solution for 4.58^2=3.3^2+3.3^2-2(3.3)(3.3)cos(x) ?
The general solution for 4.58^2=3.3^2+3.3^2-2(3.3)(3.3)cos(x) is x=1.53389…+2pin,x=2pi-1.53389…+2pin