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58.2^2=25.8^2+33.4^2-2(25.8(33.4))cos(a)

Solution

58. 2^{2} = 25. 8^{2} + 33. 4^{2} - 2 (25.8 (33.4)) cos (a)

a = 2.77035 \dots + 2 πn, a = - 2.77035 \dots + 2 πn

Degrees

a = 158.72986 \dots^{\circ} + 36 0^{\circ} n, a = - 158.72986 \dots^{\circ} + 36 0^{\circ} n

Solution steps

58. 2^{2} = 25. 8^{2} + 33. 4^{2} - 2 (25.8 (33.4)) cos (a)

Switch sides

25. 8^{2} + 33. 4^{2} - 2 \cdot 25.8 \cdot 33.4 cos (a) = 58. 2^{2}

Multiply the numbers:

2 \cdot 25.8 \cdot 33.4 = 1723.44

25. 8^{2} + 33. 4^{2} - 1723.44 cos (a) = 58. 2^{2}

25. 8^{2} = 665.64

665.64 + 33. 4^{2} - 1723.44 cos (a) = 58. 2^{2}

33. 4^{2} = 1115.56

665.64 + 1115.56 - 1723.44 cos (a) = 58. 2^{2}

Add the numbers:

665.64 + 1115.56 = 1781.2

- 1723.44 cos (a) + 1781.2 = 58. 2^{2}

58. 2^{2} = 3387.24

- 1723.44 cos (a) + 1781.2 = 3387.24

Multiply both sides by

100

- 1723.44 cos (a) + 1781.2 = 3387.24

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

- 1723.44 cos (a) \cdot 100 + 1781.2 \cdot 100 = 3387.24 \cdot 100

Refine

- 172344 cos (a) + 178120 = 338724

- 172344 cos (a) + 178120 = 338724

Move

178120

to the right side

- 172344 cos (a) + 178120 = 338724

Subtract

178120

from both sides

- 172344 cos (a) + 178120 - 178120 = 338724 - 178120

Simplify

- 172344 cos (a) = 160604

- 172344 cos (a) = 160604

Divide both sides by

- 172344

- 172344 cos (a) = 160604

Divide both sides by

- 172344

\frac{- 172344 cos ( a )}{- 172344} = \frac{160604}{- 172344}

Simplify

\frac{- 172344 cos ( a )}{- 172344} = \frac{160604}{- 172344}

Simplify

\frac{- 172344 cos ( a )}{- 172344} : cos (a)

\frac{- 172344 cos ( a )}{- 172344}

Apply the fraction rule:

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

= \frac{172344 cos ( a )}{172344}

Divide the numbers:

\frac{172344}{172344} = 1

= cos (a)

Simplify

\frac{160604}{- 172344} : - \frac{40151}{43086}

\frac{160604}{- 172344}

Apply the fraction rule:

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

= - \frac{160604}{172344}

Cancel the common factor:

4

= - \frac{40151}{43086}

cos (a) = - \frac{40151}{43086}

cos (a) = - \frac{40151}{43086}

cos (a) = - \frac{40151}{43086}

Apply trig inverse properties

cos (a) = - \frac{40151}{43086}

General solutions for

cos (a) = - \frac{40151}{43086}

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

a = arccos (- \frac{40151}{43086}) + 2 πn, a = - arccos (- \frac{40151}{43086}) + 2 πn

a = arccos (- \frac{40151}{43086}) + 2 πn, a = - arccos (- \frac{40151}{43086}) + 2 πn

Show solutions in decimal form

a = 2.77035 \dots + 2 πn, a = - 2.77035 \dots + 2 πn

tan (θ) = - 3, 0 \leq θ \leq 2 π

4 cos (θ) - 1 = 2 sin (θ) tan (θ)

3 tan (θ) = tan (2 θ)

cos^{(2)} (x) - 3 sin^{(2)} (x) = 0

a, cos (a) cos (b) = 0.426