What is the value of e^{-pi/2}sin(pi/2) ?

The value of e^{-pi/2}sin(pi/2) is 1/(e^{pi/2)}

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e^{-pi/2}sin(pi/2)

e^{- \frac{π}{2}} sin (\frac{π}{2})

\frac{1}{e ^{\frac{π}{2}}}

Decimal Notation

0.20787 \dots

Solution steps

e^{- \frac{π}{2}} sin (\frac{π}{2})

Use the following trivial identity:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

= e^{- \frac{π}{2}} \cdot 1

Simplify

e^{- \frac{π}{2}} \cdot 1 : \frac{1}{e ^{\frac{π}{2}}}

e^{- \frac{π}{2}} \cdot 1

Apply exponent rule:

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

e^{- \frac{π}{2}} = \frac{1}{e ^{\frac{π}{2}}}

= 1 \cdot \frac{1}{e ^{\frac{π}{2}}}

Multiply:

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

= \frac{1}{e ^{\frac{π}{2}}}

= \frac{1}{e ^{\frac{π}{2}}}

sin (3 0^{\circ}) - cos (4 5^{\circ})

\frac{6.47}{sec ( 2 0 ^{\circ} )}

tan (arctan (\frac{1}{3}))

cot (3 0^{\circ}) - sin (4 5^{\circ})

cos (2.2)

What is the value of e^{-pi/2}sin(pi/2) ?
The value of e^{-pi/2}sin(pi/2) is 1/(e^{pi/2)}