What is the general solution for 18^2=8^2+20^2-2*8*20*cos(x) ?

The general solution for 18^2=8^2+20^2-2*8*20*cos(x) is x=1.11797…+2pin,x=2pi-1.11797…+2pin

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18^2=8^2+20^2-2820*cos(x)

1 8^{2} = 8^{2} + 2 0^{2} - 2 \cdot 8 \cdot 20 \cdot cos (x)

x = 1.11797 \dots + 2 πn, x = 2 π - 1.11797 \dots + 2 πn

Solution steps

1 8^{2} = 8^{2} + 2 0^{2} - 2 \cdot 8 \cdot 20 cos (x)

Switch sides

8^{2} + 2 0^{2} - 2 \cdot 8 \cdot 20 cos (x) = 1 8^{2}

Multiply the numbers:

2 \cdot 8 \cdot 20 = 320

8^{2} + 2 0^{2} - 320 cos (x) = 1 8^{2}

8^{2} = 64

64 + 2 0^{2} - 320 cos (x) = 1 8^{2}

2 0^{2} = 400

64 + 400 - 320 cos (x) = 1 8^{2}

Add the numbers:

64 + 400 = 464

- 320 cos (x) + 464 = 1 8^{2}

1 8^{2} = 324

- 320 cos (x) + 464 = 324

Move

464

to the right side

- 320 cos (x) = - 140

Divide both sides by

- 320

cos (x) = \frac{7}{16}

Apply trig inverse properties

x = arccos (\frac{7}{16}) + 2 πn, x = 2 π - arccos (\frac{7}{16}) + 2 πn

Show solutions in decimal form

x = 1.11797 \dots + 2 πn, x = 2 π - 1.11797 \dots + 2 πn

cot (θ) = - \frac{π}{6}

3 tan^{2} (x) - 3 tan (x) = 0

2 sin^{2} (x) + 2 sin (x) + 1 = 0

4 cos (x) - 6 sin (x) = 3

sin (x) = 0.64

What is the general solution for 18^2=8^2+20^2-2*8*20*cos(x) ?
The general solution for 18^2=8^2+20^2-2*8*20*cos(x) is x=1.11797…+2pin,x=2pi-1.11797…+2pin