What is the value of (-113100)/(320.96*cos(180)) ?

The value of (-113100)/(320.96*cos(180)) is 706875/2006

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(-113100)/(320.96*cos(180))

\frac{- 113100}{320.96 \cdot cos ( 18 0 ^{\circ} )}

\frac{706875}{2006}

Decimal Notation

352.38035 \dots

Solution steps

\frac{- 113100}{320.96 cos ( 18 0 ^{\circ} )}

= \frac{- 113100}{\frac{8024}{25} cos ( 18 0 ^{\circ} )}

Use the following trivial identity:

cos (18 0^{\circ}) = (- 1)

cos (18 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= (- 1)

= \frac{- 113100}{\frac{8024}{25} ( - 1 )}

Simplify

\frac{- 113100}{\frac{8024}{25} ( - 1 )} : \frac{706875}{2006}

\frac{- 113100}{\frac{8024}{25} ( - 1 )}

Remove parentheses:

(- a) = - a

= \frac{- 113100}{- \frac{8024}{25} \cdot 1}

Multiply:

\frac{8024}{25} \cdot 1 = \frac{8024}{25}

= \frac{- 113100}{- \frac{8024}{25}}

Apply the fraction rule:

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

= \frac{113100}{\frac{8024}{25}}

Apply the fraction rule:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= \frac{113100 \cdot 25}{8024}

Multiply the numbers:

113100 \cdot 25 = 2827500

= \frac{2827500}{8024}

Cancel the common factor:

4

= \frac{706875}{2006}

= \frac{706875}{2006}

\frac{5}{tan ( 3 1 ^{\circ} )}

4 cos^{2} (\frac{- π}{4})

cot (- \frac{13 π}{4})

1 - 2 sin^{2} (\frac{3 π}{7})

sec^{2} (7 0^{\circ})

What is the value of (-113100)/(320.96*cos(180)) ?
The value of (-113100)/(320.96*cos(180)) is 706875/2006