What is the value of (28)/(cos(45)) ?

The value of (28)/(cos(45)) is 28sqrt(2)

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(28)/(cos(45))

\frac{28}{cos ( 4 5 ^{\circ} )}

282

Decimal Notation

39.59797 \dots

Solution steps

\frac{28}{cos ( 4 5 ^{\circ} )}

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\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{2}{2}

= \frac{28}{\frac{2}{2}}

Simplify

\frac{28}{\frac{2}{2}} : 282

\frac{28}{\frac{2}{2}}

Apply the fraction rule:

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

= \frac{28 \cdot 2}{2}

Multiply the numbers:

28 \cdot 2 = 56

= \frac{56}{2}

Factor

56 : 2^{3} \cdot 7

Factor

56 = 2^{3} \cdot 7

= \frac{2 ^{3} \cdot 7}{2}

Cancel

\frac{2 ^{3} \cdot 7}{2} : 7 \cdot 2^{\frac{5}{2}}

\frac{2 ^{3} \cdot 7}{2}

Apply radical rule:

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

= \frac{2 ^{3} \cdot 7}{2 ^{\frac{1}{2}}}

Apply exponent rule:

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

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

= 7 \cdot 2^{- \frac{1}{2} + 3}

Subtract the numbers:

3 - \frac{1}{2} = \frac{5}{2}

= 7 \cdot 2^{\frac{5}{2}}

= 7 \cdot 2^{\frac{5}{2}}

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

2^{\frac{5}{2}}

2^{\frac{5}{2}} = 2^{2 + \frac{1}{2}}

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

Apply exponent rule:

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

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

Refine

= 2^{2} 2

= 7 \cdot 2^{2} 2

2^{2} = 4

= 7 \cdot 42

Multiply the numbers:

7 \cdot 4 = 28

= 282

= 282

arctan (\frac{9}{23})

sec (π) \cdot tan (π)

cot (\frac{7}{4})

arcsin (csc (- \frac{π}{2}))

\frac{arctan ( 0 )}{1}