What is the value of (8.2)/(cos(72)) ?

The value of (8.2)/(cos(72)) is (41(1+sqrt(5)))/5

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(8.2)/(cos(72))

\frac{8.2}{cos ( 7 2 ^{\circ} )}

\frac{41 ( 1 + 5 )}{5}

Solution steps

\frac{8.2}{cos ( 7 2 ^{\circ} )}

= \frac{\frac{41}{5}}{cos ( 7 2 ^{\circ} )}

Simplify

= \frac{41}{5 cos ( 7 2 ^{\circ} )}

Rewrite using trig identities:

cos (7 2^{\circ}) = 1 - 2 sin^{2} (3 6^{\circ})

= \frac{41}{5 ( 1 - 2 sin ^{2} ( 3 6 ^{\circ} ) )}

Rewrite using trig identities:

sin (3 6^{\circ}) = \frac{2 5 - 5}{4}

= \frac{41}{5 ( 1 - 2 ( \frac{2 5 - 5}{4} ) ^{2} )}

Simplify

\frac{41}{5 ( 1 - 2 ( \frac{2 5 - 5}{4} ) ^{2} )} : \frac{41 ( 1 + 5 )}{5}

= \frac{41 ( 1 + 5 )}{5}

sin (\frac{1}{- 1})

cos (2 arctan (\frac{1}{7}) + arcsin (\frac{3}{7}))

sin (arctan (\frac{- 12}{5}))

2 sin (0) cos (0)

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

What is the value of (8.2)/(cos(72)) ?
The value of (8.2)/(cos(72)) is (41(1+sqrt(5)))/5