What is the value of (113)/(36.5*cos(30)) ?

The value of (113)/(36.5*cos(30)) is (452sqrt(3))/(219)

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(113)/(36.5*cos(30))

\frac{113}{36.5 \cdot cos ( 3 0 ^{\circ} )}

\frac{452 3}{219}

Decimal Notation

3.57482 \dots

Solution steps

\frac{113}{36.5 cos ( 3 0 ^{\circ} )}

= \frac{113}{\frac{73}{2} cos ( 3 0 ^{\circ} )}

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 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}

= \frac{3}{2}

= \frac{113}{\frac{73}{2} \cdot \frac{3}{2}}

Simplify

\frac{113}{\frac{73}{2} \cdot \frac{3}{2}} : \frac{452 3}{219}

\frac{113}{\frac{73}{2} \cdot \frac{3}{2}}

Multiply

\frac{73}{2} \cdot \frac{3}{2} : \frac{73 3}{4}

\frac{73}{2} \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{73 3}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{73 3}{4}

= \frac{113}{\frac{73 3}{4}}

Apply the fraction rule:

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

= \frac{113 \cdot 4}{73 3}

Multiply the numbers:

113 \cdot 4 = 452

= \frac{452}{73 3}

Rationalize

\frac{452}{73 3} : \frac{452 3}{219}

\frac{452}{73 3}

Multiply by the conjugate

\frac{3}{3}

= \frac{452 3}{73 3 3}

7333 = 219

7333

Apply radical rule:

a a = a

33 = 3

= 73 \cdot 3

Multiply the numbers:

73 \cdot 3 = 219

= 219

= \frac{452 3}{219}

= \frac{452 3}{219}

= \frac{452 3}{219}

\frac{sin ( 301 5 ^{\circ} ) tan ( 429 0 ^{\circ} )}{cos ( 273 0 ^{\circ} )}

sinh (- arccosh (2))

sin (\frac{π}{9}) - sin (\frac{2 π}{9}) - sin (\frac{3 π}{9}) + sin (\frac{4 π}{9})

44 sin (2 8^{\circ})

- 3 cos (\frac{1}{2} \cdot 0)

What is the value of (113)/(36.5*cos(30)) ?
The value of (113)/(36.5*cos(30)) is (452sqrt(3))/(219)