What is the value of e^{pi/4}sin(pi/4) ?

The value of e^{pi/4}sin(pi/4) is (e^{pi/4})/(2^{1/2)}

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e^{pi/4}sin(pi/4)

e^{\frac{π}{4}} sin (\frac{π}{4})

\frac{e ^{\frac{π}{4}}}{2 ^{\frac{1}{2}}}

Decimal Notation

1.55088 \dots

Solution steps

e^{\frac{π}{4}} sin (\frac{π}{4})

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

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{2}{2}

= e^{\frac{π}{4}} \frac{2}{2}

Simplify

e^{\frac{π}{4}} \frac{2}{2} : \frac{e ^{\frac{π}{4}}}{2 ^{\frac{1}{2}}}

e^{\frac{π}{4}} \frac{2}{2}

\frac{2}{2} = \frac{1}{2 ^{\frac{1}{2}}}

\frac{2}{2}

Apply exponent rule:

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

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

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

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{1}{2 ^{\frac{1}{2}}}

= e^{\frac{π}{4}} \frac{1}{2 ^{\frac{1}{2}}}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot e ^{\frac{π}{4}}}{2 ^{\frac{1}{2}}}

Multiply:

1 \cdot e^{\frac{π}{4}} = e^{\frac{π}{4}}

= \frac{e ^{\frac{π}{4}}}{2 ^{\frac{1}{2}}}

= \frac{e ^{\frac{π}{4}}}{2 ^{\frac{1}{2}}}

cos (120 π)

2 ln (sec (\frac{π}{4}))

2 cos (\frac{π}{6}) + sin (2) (\frac{π}{6})

cos (- 0)

- sin (\frac{π}{6}) + cos (\frac{π}{6})

What is the value of e^{pi/4}sin(pi/4) ?
The value of e^{pi/4}sin(pi/4) is (e^{pi/4})/(2^{1/2)}