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

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

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

e^{\frac{π}{2}} sin (\frac{π}{2})

e^{\frac{π}{2}}

Decimal Notation

4.81047 \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}}

arccot (- \frac{4}{3})

cos (13 0^{\circ}) cos (1 0^{\circ}) + sin (13 0^{\circ}) sin (1 0^{\circ})

\frac{8}{cos ( 3 0 ^{\circ} )}

500 cos (2 0^{\circ})

arccos (\frac{- 1}{3})

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