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Beliebt Trigonometrie >

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

Lösung

e^{\frac{π}{4}} cos (\frac{π}{4})

Lösung

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

+1

Dezimale

1.55088 \dots

Schritte zur Lösung

e^{\frac{π}{4}} cos (\frac{π}{4})

Verwende die folgende triviale Identität:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{π}{4})

cos (x)

Periodizitätstabelle mit

2 πn

Zyklus:

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

= \frac{2}{2}

= e^{\frac{π}{4}} \frac{2}{2}

Vereinfache

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}

Wende Exponentenregel an:

\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}}}

Subtrahiere die Zahlen:

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

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

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

Multipliziere Brüche:

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

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

Multipliziere:

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}}}

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