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Popular >

12^{(2)}=13^{(2)}+5^{(2)}-2(13)(5)cos(B)

Solution

1 2^{(2)} = 1 3^{(2)} + 5^{(2)} - 2 (13) (5) cos (B)

B = 1.17600 \dots + 2 πn, B = 2 π - 1.17600 \dots + 2 πn

Degrees

B = 67.38013 \dots^{\circ} + 36 0^{\circ} n, B = 292.61986 \dots^{\circ} + 36 0^{\circ} n

Solution steps

1 2^{(2)} = 1 3^{(2)} + 5^{(2)} - 2 (13) (5) cos (B)

Switch sides

1 3^{2} + 5^{2} - 2 \cdot 13 \cdot 5 cos (B) = 1 2^{2}

Multiply the numbers:

2 \cdot 13 \cdot 5 = 130

1 3^{2} + 5^{2} - 130 cos (B) = 1 2^{2}

1 3^{2} = 169

169 + 5^{2} - 130 cos (B) = 1 2^{2}

5^{2} = 25

169 + 25 - 130 cos (B) = 1 2^{2}

Add the numbers:

169 + 25 = 194

- 130 cos (B) + 194 = 1 2^{2}

1 2^{2} = 144

- 130 cos (B) + 194 = 144

Move

194

to the right side

- 130 cos (B) + 194 = 144

Subtract

194

from both sides

- 130 cos (B) + 194 - 194 = 144 - 194

Simplify

- 130 cos (B) = - 50

- 130 cos (B) = - 50

Divide both sides by

- 130

- 130 cos (B) = - 50

Divide both sides by

- 130

\frac{- 130 cos ( B )}{- 130} = \frac{- 50}{- 130}

Simplify

\frac{- 130 cos ( B )}{- 130} = \frac{- 50}{- 130}

Simplify

\frac{- 130 cos ( B )}{- 130} : cos (B)

\frac{- 130 cos ( B )}{- 130}

Apply the fraction rule:

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

= \frac{130 cos ( B )}{130}

Divide the numbers:

\frac{130}{130} = 1

= cos (B)

Simplify

\frac{- 50}{- 130} : \frac{5}{13}

\frac{- 50}{- 130}

Apply the fraction rule:

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

= \frac{50}{130}

Cancel the common factor:

10

= \frac{5}{13}

cos (B) = \frac{5}{13}

cos (B) = \frac{5}{13}

cos (B) = \frac{5}{13}

Apply trig inverse properties

cos (B) = \frac{5}{13}

General solutions for

cos (B) = \frac{5}{13}

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

B = arccos (\frac{5}{13}) + 2 πn, B = 2 π - arccos (\frac{5}{13}) + 2 πn

B = arccos (\frac{5}{13}) + 2 πn, B = 2 π - arccos (\frac{5}{13}) + 2 πn

Show solutions in decimal form

B = 1.17600 \dots + 2 πn, B = 2 π - 1.17600 \dots + 2 πn

tan (6 t) = 2

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

(cos (x) = 1) = (sec (x) = 1)

cot (\frac{x}{3}) = \frac{- 1}{3}

cos^{2} (θ) = sin^{2} (θ) + 1, 0^{\circ} \leq θ \leq 36 0^{\circ}