What is the general solution for 12^2=10^2+12^2-2(10)(12)cos(b) ?

The general solution for 12^2=10^2+12^2-2(10)(12)cos(b) is b=1.14102…+2pin,b=2pi-1.14102…+2pin

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Popular >

12^2=10^2+12^2-2(10)(12)cos(b)

Solution

1 2^{2} = 1 0^{2} + 1 2^{2} - 2 (10) (12) cos (b)

Solution

b = 1.14102 \dots + 2 πn, b = 2 π - 1.14102 \dots + 2 πn

Degrees

b = 65.37568 \dots^{\circ} + 36 0^{\circ} n, b = 294.62431 \dots^{\circ} + 36 0^{\circ} n

Solution steps

1 2^{2} = 1 0^{2} + 1 2^{2} - 2 (10) (12) cos (b)

Switch sides

1 0^{2} + 1 2^{2} - 2 \cdot 10 \cdot 12 cos (b) = 1 2^{2}

Subtract

1 2^{2}

from both sides

1 0^{2} + 1 2^{2} - 2 \cdot 10 \cdot 12 cos (b) - 1 2^{2} = 1 2^{2} - 1 2^{2}

Simplify

1 0^{2} - 2 \cdot 10 \cdot 12 cos (b) = 0

Multiply the numbers:

2 \cdot 10 \cdot 12 = 240

1 0^{2} - 240 cos (b) = 0

1 0^{2} = 100

100 - 240 cos (b) = 0

Move

100

to the right side

100 - 240 cos (b) = 0

Subtract

100

from both sides

100 - 240 cos (b) - 100 = 0 - 100

Simplify

- 240 cos (b) = - 100

- 240 cos (b) = - 100

Divide both sides by

- 240

- 240 cos (b) = - 100

Divide both sides by

- 240

\frac{- 240 cos ( b )}{- 240} = \frac{- 100}{- 240}

Simplify

\frac{- 240 cos ( b )}{- 240} = \frac{- 100}{- 240}

Simplify

\frac{- 240 cos ( b )}{- 240} : cos (b)

\frac{- 240 cos ( b )}{- 240}

Apply the fraction rule:

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

= \frac{240 cos ( b )}{240}

Divide the numbers:

\frac{240}{240} = 1

= cos (b)

Simplify

\frac{- 100}{- 240} : \frac{5}{12}

\frac{- 100}{- 240}

Apply the fraction rule:

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

= \frac{100}{240}

Cancel the common factor:

20

= \frac{5}{12}

cos (b) = \frac{5}{12}

cos (b) = \frac{5}{12}

cos (b) = \frac{5}{12}

Apply trig inverse properties

cos (b) = \frac{5}{12}

General solutions for

cos (b) = \frac{5}{12}

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

b = arccos (\frac{5}{12}) + 2 πn, b = 2 π - arccos (\frac{5}{12}) + 2 πn

b = arccos (\frac{5}{12}) + 2 πn, b = 2 π - arccos (\frac{5}{12}) + 2 πn

Show solutions in decimal form

b = 1.14102 \dots + 2 πn, b = 2 π - 1.14102 \dots + 2 πn

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Frequently Asked Questions (FAQ)

What is the general solution for 12^2=10^2+12^2-2(10)(12)cos(b) ?
The general solution for 12^2=10^2+12^2-2(10)(12)cos(b) is b=1.14102…+2pin,b=2pi-1.14102…+2pin