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

解

e^{\frac{π}{4}} sin (\frac{π}{4})

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

十進法表記

1.55088 \dots

解答ステップ

e^{\frac{π}{4}} sin (\frac{π}{4})

次の自明恒等式を使用する:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

sin (x)

2 πn

循環を含む周期性テーブル:

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}

簡素化

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}

指数の規則を適用する:

\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}}}

数を引く:

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

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

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

分数を乗じる:

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

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

乗算:

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}}}