What is the general solution for 12^2=15^2+20^2-2(15)(20)(cos(a)) ?

The general solution for 12^2=15^2+20^2-2(15)(20)(cos(a)) is a=0.64071…+2pin,a=2pi-0.64071…+2pin

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12^2=15^2+20^2-2(15)(20)(cos(a))

1 2^{2} = 1 5^{2} + 2 0^{2} - 2 (15) (20) (cos (a))

a = 0.64071 \dots + 2 πn, a = 2 π - 0.64071 \dots + 2 πn

Degrees

a = 36.71044 \dots^{\circ} + 36 0^{\circ} n, a = 323.28955 \dots^{\circ} + 36 0^{\circ} n

Solution steps

1 2^{2} = 1 5^{2} + 2 0^{2} - 2 (15) (20) (cos (a))

Switch sides

1 5^{2} + 2 0^{2} - 2 \cdot 15 \cdot 20 cos (a) = 1 2^{2}

Multiply the numbers:

2 \cdot 15 \cdot 20 = 600

1 5^{2} + 2 0^{2} - 600 cos (a) = 1 2^{2}

1 5^{2} = 225

225 + 2 0^{2} - 600 cos (a) = 1 2^{2}

2 0^{2} = 400

225 + 400 - 600 cos (a) = 1 2^{2}

Add the numbers:

225 + 400 = 625

- 600 cos (a) + 625 = 1 2^{2}

1 2^{2} = 144

- 600 cos (a) + 625 = 144

Move

625

to the right side

- 600 cos (a) + 625 = 144

Subtract

625

from both sides

- 600 cos (a) + 625 - 625 = 144 - 625

Simplify

- 600 cos (a) = - 481

- 600 cos (a) = - 481

Divide both sides by

- 600

- 600 cos (a) = - 481

Divide both sides by

- 600

\frac{- 600 cos ( a )}{- 600} = \frac{- 481}{- 600}

Simplify

cos (a) = \frac{481}{600}

cos (a) = \frac{481}{600}

Apply trig inverse properties

cos (a) = \frac{481}{600}

General solutions for

cos (a) = \frac{481}{600}

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

a = arccos (\frac{481}{600}) + 2 πn, a = 2 π - arccos (\frac{481}{600}) + 2 πn

a = arccos (\frac{481}{600}) + 2 πn, a = 2 π - arccos (\frac{481}{600}) + 2 πn

Show solutions in decimal form

a = 0.64071 \dots + 2 πn, a = 2 π - 0.64071 \dots + 2 πn

0.428 = cos (1.57 \cdot x - π)

5 = 10 sin (a)

sin (θ) = cos (2 θ + 5 4^{\circ})

t, y = cos (t)

x, r^{2} = 9 cos (2 x)

What is the general solution for 12^2=15^2+20^2-2(15)(20)(cos(a)) ?
The general solution for 12^2=15^2+20^2-2(15)(20)(cos(a)) is a=0.64071…+2pin,a=2pi-0.64071…+2pin