What is the general solution for 20^2=13^2+9^2-2(13)(9)*cos(a) ?

The general solution for 20^2=13^2+9^2-2(13)(9)*cos(a) is a=2.26663…+2pin,a=-2.26663…+2pin

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20^2=13^2+9^2-2(13)(9)*cos(a)

2 0^{2} = 1 3^{2} + 9^{2} - 2 (13) (9) \cdot cos (a)

a = 2.26663 \dots + 2 πn, a = - 2.26663 \dots + 2 πn

Degrees

a = 129.86834 \dots^{\circ} + 36 0^{\circ} n, a = - 129.86834 \dots^{\circ} + 36 0^{\circ} n

Solution steps

2 0^{2} = 1 3^{2} + 9^{2} - 2 (13) (9) cos (a)

Switch sides

1 3^{2} + 9^{2} - 2 \cdot 13 \cdot 9 cos (a) = 2 0^{2}

Multiply the numbers:

2 \cdot 13 \cdot 9 = 234

1 3^{2} + 9^{2} - 234 cos (a) = 2 0^{2}

1 3^{2} = 169

169 + 9^{2} - 234 cos (a) = 2 0^{2}

9^{2} = 81

169 + 81 - 234 cos (a) = 2 0^{2}

Add the numbers:

169 + 81 = 250

- 234 cos (a) + 250 = 2 0^{2}

2 0^{2} = 400

- 234 cos (a) + 250 = 400

Move

250

to the right side

- 234 cos (a) + 250 = 400

Subtract

250

from both sides

- 234 cos (a) + 250 - 250 = 400 - 250

Simplify

- 234 cos (a) = 150

- 234 cos (a) = 150

Divide both sides by

- 234

- 234 cos (a) = 150

Divide both sides by

- 234

\frac{- 234 cos ( a )}{- 234} = \frac{150}{- 234}

Simplify

\frac{- 234 cos ( a )}{- 234} = \frac{150}{- 234}

Simplify

\frac{- 234 cos ( a )}{- 234} : cos (a)

\frac{- 234 cos ( a )}{- 234}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{234 cos ( a )}{234}

Divide the numbers:

\frac{234}{234} = 1

= cos (a)

Simplify

\frac{150}{- 234} : - \frac{25}{39}

\frac{150}{- 234}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{150}{234}

Cancel the common factor:

6

= - \frac{25}{39}

cos (a) = - \frac{25}{39}

cos (a) = - \frac{25}{39}

cos (a) = - \frac{25}{39}

Apply trig inverse properties

cos (a) = - \frac{25}{39}

General solutions for

cos (a) = - \frac{25}{39}

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

a = arccos (- \frac{25}{39}) + 2 πn, a = - arccos (- \frac{25}{39}) + 2 πn

a = arccos (- \frac{25}{39}) + 2 πn, a = - arccos (- \frac{25}{39}) + 2 πn

Show solutions in decimal form

a = 2.26663 \dots + 2 πn, a = - 2.26663 \dots + 2 πn

t, 4 cos (2 t) + 1 = 3

cos (2 x) - 3 cos (- x) + 2 = 0

tan (x) + cot (x) = \frac{5}{2}

sin (2 x) + 2 cos (x) = 0

cos (\frac{x}{2}) - sin (\frac{x}{2}) = 0

What is the general solution for 20^2=13^2+9^2-2(13)(9)*cos(a) ?
The general solution for 20^2=13^2+9^2-2(13)(9)*cos(a) is a=2.26663…+2pin,a=-2.26663…+2pin