What is the value of (72)/(cos(30)) ?

The value of (72)/(cos(30)) is 48sqrt(3)

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(72)/(cos(30))

\frac{72}{cos ( 3 0 ^{\circ} )}

483

Decimal Notation

83.13843 \dots

Solution steps

\frac{72}{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{72}{\frac{3}{2}}

Simplify

\frac{72}{\frac{3}{2}} : 483

\frac{72}{\frac{3}{2}}

Apply the fraction rule:

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

= \frac{72 \cdot 2}{3}

Multiply the numbers:

72 \cdot 2 = 144

= \frac{144}{3}

Factor

144 : 2^{4} \cdot 3^{2}

Factor

144 = 2^{4} \cdot 3^{2}

= \frac{2 ^{4} \cdot 3 ^{2}}{3}

Cancel

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

\frac{2 ^{4} \cdot 3 ^{2}}{3}

Apply radical rule:

3 = 3^{\frac{1}{2}}

= \frac{2 ^{4} \cdot 3 ^{2}}{3 ^{\frac{1}{2}}}

Apply exponent rule:

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

\frac{3 ^{2}}{3 ^{\frac{1}{2}}} = 3^{2 - \frac{1}{2}}

= 2^{4} \cdot 3^{- \frac{1}{2} + 2}

Subtract the numbers:

2 - \frac{1}{2} = \frac{3}{2}

= 2^{4} \cdot 3^{\frac{3}{2}}

= 2^{4} \cdot 3^{\frac{3}{2}}

3^{\frac{3}{2}} = 33

3^{\frac{3}{2}}

3^{\frac{3}{2}} = 3^{1 + \frac{1}{2}}

= 3^{1 + \frac{1}{2}}

Apply exponent rule:

x^{a + b} = x^{a} x^{b}

= 3^{1} \cdot 3^{\frac{1}{2}}

Refine

= 33

= 2^{4} \cdot 33

2^{4} = 16

= 16 \cdot 33

Multiply the numbers:

16 \cdot 3 = 48

= 483

= 483

e^{6.3} (- sin (6.3) + cos (6.3))

arccos (1.04)

arctan (\frac{13}{12})

\frac{sin ( 3 5 ^{\circ} )}{sin ( 2 5 ^{\circ} )}

arccos (1.15)