What is the value of e^{-cos(pi)} ?

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e^{-cos(pi)}

e^{- c o s (π)}

e

Decimal Notation

2.71828 \dots

Solution steps

e^{- c o s (π)}

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= (- 1)

= e^{- (- 1)}

Simplify

= e

\frac{1}{2} (cos^{2} (2 2^{\circ})) (cos^{2} (2 2^{\circ}))

4 5^{2} + 1 1^{2} - 2 (45) (11) cos (2 5^{\circ})

arccos (37)

\frac{7 sin ( 3 9 ^{\circ} )}{tan ( 5 0 ^{\circ} )}

arctan (tan (\frac{17 π}{20}))