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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Popular Trigonometry >

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

Solution

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

Solution

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

Degrees

x = 64.05552 \dots^{\circ} + 36 0^{\circ} n, x = 295.94447 \dots^{\circ} + 36 0^{\circ} n

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) + 464 = 324

Subtract

464

from both sides

- 320 cos (x) + 464 - 464 = 324 - 464

Simplify

- 320 cos (x) = - 140

- 320 cos (x) = - 140

Divide both sides by

- 320

- 320 cos (x) = - 140

Divide both sides by

- 320

\frac{- 320 cos ( x )}{- 320} = \frac{- 140}{- 320}

Simplify

\frac{- 320 cos ( x )}{- 320} = \frac{- 140}{- 320}

Simplify

\frac{- 320 cos ( x )}{- 320} : cos (x)

\frac{- 320 cos ( x )}{- 320}

Apply the fraction rule:

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

= \frac{320 cos ( x )}{320}

Divide the numbers:

\frac{320}{320} = 1

= cos (x)

Simplify

\frac{- 140}{- 320} : \frac{7}{16}

\frac{- 140}{- 320}

Apply the fraction rule:

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

= \frac{140}{320}

Cancel the common factor:

20

= \frac{7}{16}

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

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

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

Apply trig inverse properties

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

General solutions for

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

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

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

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

Graph

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Frequently Asked Questions (FAQ)

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