What is the value of e^0sin(pi/3) ?

The value of e^0sin(pi/3) is (sqrt(3))/2

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e^0sin(pi/3)

e^{0} sin (\frac{π}{3})

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

e^{0} sin (\frac{π}{3})

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

sin (\frac{π}{3})

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}

= \frac{3}{2}

= e^{0} \frac{3}{2}

Simplify

= \frac{3}{2}

cos (2 arcsin (- \frac{5}{13}))

tan (\frac{π}{3}) + cos (\frac{5 π}{6}) \cdot sin (- \frac{3 π}{4})

cos^{2} (6 7^{\circ})

sin (2 π) - sin (0)

csc (- \frac{13 π}{4})