What is the general solution for 27^2=56^2+35^2-(2*56*35*cos(x)) ?

The general solution for 27^2=56^2+35^2-(2*56*35*cos(x)) is x=0.38571…+2pin,x=2pi-0.38571…+2pin

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27^2=56^2+35^2-(25635*cos(x))

2 7^{2} = 5 6^{2} + 3 5^{2} - (2 \cdot 56 \cdot 35 \cdot cos (x))

x = 0.38571 \dots + 2 πn, x = 2 π - 0.38571 \dots + 2 πn

Solution steps

2 7^{2} = 5 6^{2} + 3 5^{2} - (2 \cdot 56 \cdot 35 cos (x))

Switch sides

5 6^{2} + 3 5^{2} - 2 \cdot 56 \cdot 35 cos (x) = 2 7^{2}

Multiply the numbers:

2 \cdot 56 \cdot 35 = 3920

5 6^{2} + 3 5^{2} - 3920 cos (x) = 2 7^{2}

5 6^{2} = 3136

3136 + 3 5^{2} - 3920 cos (x) = 2 7^{2}

3 5^{2} = 1225

3136 + 1225 - 3920 cos (x) = 2 7^{2}

Add the numbers:

3136 + 1225 = 4361

- 3920 cos (x) + 4361 = 2 7^{2}

2 7^{2} = 729

- 3920 cos (x) + 4361 = 729

Move

4361

to the right side

- 3920 cos (x) = - 3632

Divide both sides by

- 3920

cos (x) = \frac{227}{245}

Apply trig inverse properties

x = arccos (\frac{227}{245}) + 2 πn, x = 2 π - arccos (\frac{227}{245}) + 2 πn

Show solutions in decimal form

x = 0.38571 \dots + 2 πn, x = 2 π - 0.38571 \dots + 2 πn

x, sin^{2} (x) - sin (x) - 2 = 0

cos (x - \frac{2 π}{3}) = \frac{1}{2}

3 sin (θ) = 3

cos (2 θ) + sin (θ) = 0, 0 \leq θ < 2 π

cos (\frac{π}{3} x - \frac{π}{4}) = \frac{2}{2}

What is the general solution for 27^2=56^2+35^2-(2*56*35*cos(x)) ?
The general solution for 27^2=56^2+35^2-(2*56*35*cos(x)) is x=0.38571…+2pin,x=2pi-0.38571…+2pin