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Popular >

e^{cos(pi)}

Solution

e^{c o s (π)}

Solution

\frac{1}{e}

+1

Decimal Notation

0.36787 \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^{- 1} : \frac{1}{e}

e^{- 1}

Apply exponent rule:

a^{- 1} = \frac{1}{a}

= \frac{1}{e}

= \frac{1}{e}

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Frequently Asked Questions (FAQ)

What is the value of e^{cos(pi)} ?
The value of e^{cos(pi)} is 1/e