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Beliebt Trigonometrie >

cos(pi/2-x)= 4/5

Lösung

cos (\frac{π}{2} - x) = \frac{4}{5}

Lösung

x = - 2 πn + \frac{π}{2} - 0.64350 \dots, x = - 2 π - 2 πn + \frac{π}{2} + 0.64350 \dots

Grad

x = 53.13010 \dots^{\circ} - 36 0^{\circ} n, x = - 233.13010 \dots^{\circ} - 36 0^{\circ} n

Schritte zur Lösung

cos (\frac{π}{2} - x) = \frac{4}{5}

Wende die Eigenschaften der Trigonometrie an

cos (\frac{π}{2} - x) = \frac{4}{5}

Allgemeine Lösung für

cos (\frac{π}{2} - x) = \frac{4}{5}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

\frac{π}{2} - x = arccos (\frac{4}{5}) + 2 πn, \frac{π}{2} - x = 2 π - arccos (\frac{4}{5}) + 2 πn

\frac{π}{2} - x = arccos (\frac{4}{5}) + 2 πn, \frac{π}{2} - x = 2 π - arccos (\frac{4}{5}) + 2 πn

Löse

\frac{π}{2} - x = arccos (\frac{4}{5}) + 2 πn : x = - 2 πn + \frac{π}{2} - arccos (\frac{4}{5})

\frac{π}{2} - x = arccos (\frac{4}{5}) + 2 πn

Verschiebe

\frac{π}{2}

auf die rechte Seite

\frac{π}{2} - x = arccos (\frac{4}{5}) + 2 πn

Subtrahiere

\frac{π}{2}

von beiden Seiten

\frac{π}{2} - x - \frac{π}{2} = arccos (\frac{4}{5}) + 2 πn - \frac{π}{2}

Vereinfache

- x = arccos (\frac{4}{5}) + 2 πn - \frac{π}{2}

- x = arccos (\frac{4}{5}) + 2 πn - \frac{π}{2}

Teile beide Seiten durch

- 1

- x = arccos (\frac{4}{5}) + 2 πn - \frac{π}{2}

Teile beide Seiten durch

- 1

\frac{- x}{- 1} = \frac{arccos ( \frac{4}{5} )}{- 1} + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1}

Vereinfache

\frac{- x}{- 1} = \frac{arccos ( \frac{4}{5} )}{- 1} + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1}

Vereinfache

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Wende Bruchregel an:

\frac{- a}{- b} = \frac{a}{b}

= \frac{x}{1}

Wende Regel an

\frac{a}{1} = a

= x

Vereinfache

\frac{arccos ( \frac{4}{5} )}{- 1} + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1} : - 2 πn + \frac{π}{2} - arccos (\frac{4}{5})

\frac{arccos ( \frac{4}{5} )}{- 1} + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1}

Fasse gleiche Terme zusammen

= \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1} + \frac{arccos ( \frac{4}{5} )}{- 1}

\frac{2 πn}{- 1} = - 2 πn

\frac{2 πn}{- 1}

Wende Bruchregel an:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2 πn}{1}

Wende Regel an

\frac{a}{1} = a

= - 2 πn

= - 2 πn - \frac{\frac{π}{2}}{- 1} + \frac{arccos ( \frac{4}{5} )}{- 1}

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

\frac{\frac{π}{2}}{- 1}

Wende Bruchregel an:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{\frac{π}{2}}{1}

Wende Bruchregel an:

\frac{a}{1} = a

\frac{\frac{π}{2}}{1} = \frac{π}{2}

= - \frac{π}{2}

\frac{arccos ( \frac{4}{5} )}{- 1} = - arccos (\frac{4}{5})

\frac{arccos ( \frac{4}{5} )}{- 1}

Wende Bruchregel an:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{arccos ( \frac{4}{5} )}{1}

Wende Bruchregel an:

\frac{a}{1} = a

\frac{arccos ( \frac{4}{5} )}{1} = arccos (\frac{4}{5})

= - arccos (\frac{4}{5})

= - 2 πn - (- \frac{π}{2}) - arccos (\frac{4}{5})

Wende Regel an

- (- a) = a

= - 2 πn + \frac{π}{2} - arccos (\frac{4}{5})

x = - 2 πn + \frac{π}{2} - arccos (\frac{4}{5})

x = - 2 πn + \frac{π}{2} - arccos (\frac{4}{5})

x = - 2 πn + \frac{π}{2} - arccos (\frac{4}{5})

Löse

\frac{π}{2} - x = 2 π - arccos (\frac{4}{5}) + 2 πn : x = - 2 π - 2 πn + \frac{π}{2} + arccos (\frac{4}{5})

\frac{π}{2} - x = 2 π - arccos (\frac{4}{5}) + 2 πn

Verschiebe

\frac{π}{2}

auf die rechte Seite

\frac{π}{2} - x = 2 π - arccos (\frac{4}{5}) + 2 πn

Subtrahiere

\frac{π}{2}

von beiden Seiten

\frac{π}{2} - x - \frac{π}{2} = 2 π - arccos (\frac{4}{5}) + 2 πn - \frac{π}{2}

Vereinfache

- x = 2 π - arccos (\frac{4}{5}) + 2 πn - \frac{π}{2}

- x = 2 π - arccos (\frac{4}{5}) + 2 πn - \frac{π}{2}

Teile beide Seiten durch

- 1

- x = 2 π - arccos (\frac{4}{5}) + 2 πn - \frac{π}{2}

Teile beide Seiten durch

- 1

\frac{- x}{- 1} = \frac{2 π}{- 1} - \frac{arccos ( \frac{4}{5} )}{- 1} + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1}

Vereinfache

\frac{- x}{- 1} = \frac{2 π}{- 1} - \frac{arccos ( \frac{4}{5} )}{- 1} + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1}

Vereinfache

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Wende Bruchregel an:

\frac{- a}{- b} = \frac{a}{b}

= \frac{x}{1}

Wende Regel an

\frac{a}{1} = a

= x

Vereinfache

\frac{2 π}{- 1} - \frac{arccos ( \frac{4}{5} )}{- 1} + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1} : - 2 π - 2 πn + \frac{π}{2} + arccos (\frac{4}{5})

\frac{2 π}{- 1} - \frac{arccos ( \frac{4}{5} )}{- 1} + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1}

Fasse gleiche Terme zusammen

= \frac{2 π}{- 1} + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1} - \frac{arccos ( \frac{4}{5} )}{- 1}

\frac{2 π}{- 1} = - 2 π

\frac{2 π}{- 1}

Wende Bruchregel an:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2 π}{1}

Wende Regel an

\frac{a}{1} = a

= - 2 π

= - 2 π + \frac{2 πn}{- 1} - \frac{\frac{π}{2}}{- 1} - \frac{arccos ( \frac{4}{5} )}{- 1}

\frac{2 πn}{- 1} = - 2 πn

\frac{2 πn}{- 1}

Wende Bruchregel an:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2 πn}{1}

Wende Regel an

\frac{a}{1} = a

= - 2 πn

= - 2 π - 2 πn - \frac{\frac{π}{2}}{- 1} - \frac{arccos ( \frac{4}{5} )}{- 1}

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

\frac{\frac{π}{2}}{- 1}

Wende Bruchregel an:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{\frac{π}{2}}{1}

Wende Bruchregel an:

\frac{a}{1} = a

\frac{\frac{π}{2}}{1} = \frac{π}{2}

= - \frac{π}{2}

\frac{arccos ( \frac{4}{5} )}{- 1} = - arccos (\frac{4}{5})

\frac{arccos ( \frac{4}{5} )}{- 1}

Wende Bruchregel an:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{arccos ( \frac{4}{5} )}{1}

Wende Bruchregel an:

\frac{a}{1} = a

\frac{arccos ( \frac{4}{5} )}{1} = arccos (\frac{4}{5})

= - arccos (\frac{4}{5})

= - 2 π - 2 πn - (- \frac{π}{2}) - (- arccos (\frac{4}{5}))

Wende Regel an

- (- a) = a

= - 2 π - 2 πn + \frac{π}{2} + arccos (\frac{4}{5})

x = - 2 π - 2 πn + \frac{π}{2} + arccos (\frac{4}{5})

x = - 2 π - 2 πn + \frac{π}{2} + arccos (\frac{4}{5})

x = - 2 π - 2 πn + \frac{π}{2} + arccos (\frac{4}{5})

x = - 2 πn + \frac{π}{2} - arccos (\frac{4}{5}), x = - 2 π - 2 πn + \frac{π}{2} + arccos (\frac{4}{5})

Zeige Lösungen in Dezimalform

x = - 2 πn + \frac{π}{2} - 0.64350 \dots, x = - 2 π - 2 πn + \frac{π}{2} + 0.64350 \dots

Graph

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