What is the value of (90)/(cos(30)) ?

The value of (90)/(cos(30)) is 60sqrt(3)

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(90)/(cos(30))

\frac{90}{cos ( 3 0 ^{\circ} )}

603

Decimal Notation

103.92304 \dots

Solution steps

\frac{90}{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{90}{\frac{3}{2}}

Simplify

\frac{90}{\frac{3}{2}} : 603

\frac{90}{\frac{3}{2}}

Apply the fraction rule:

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

= \frac{90 \cdot 2}{3}

Multiply the numbers:

90 \cdot 2 = 180

= \frac{180}{3}

Factor

180 : 2^{2} \cdot 3^{2} \cdot 5

Factor

180 = 2^{2} \cdot 3^{2} \cdot 5

= \frac{2 ^{2} \cdot 3 ^{2} \cdot 5}{3}

Cancel

\frac{2 ^{2} \cdot 3 ^{2} \cdot 5}{3} : 2^{2} \cdot 5 \cdot 3^{\frac{3}{2}}

\frac{2 ^{2} \cdot 3 ^{2} \cdot 5}{3}

Apply radical rule:

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

= \frac{2 ^{2} \cdot 3 ^{2} \cdot 5}{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^{2} \cdot 5 \cdot 3^{- \frac{1}{2} + 2}

Subtract the numbers:

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

= 2^{2} \cdot 5 \cdot 3^{\frac{3}{2}}

= 2^{2} \cdot 5 \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^{2} \cdot 5 \cdot 33

Multiply the numbers:

5 \cdot 3 = 15

= 2^{2} \cdot 153

2^{2} = 4

= 15 \cdot 43

Multiply the numbers:

15 \cdot 4 = 60

= 603

= 603

cos (2 π)

2 + sin (2)

1.2 \cdot cos (18 \cdot 0.25 + \frac{π}{4})

\frac{3}{tan ( 4 5 ^{\circ} )}

arcsin (\frac{11}{21})