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Beliebt Trigonometrie >

arcsin((900x^2-1)/(900x^2+1))=1.18

Lösung

arcsin (\frac{900 x ^{2} - 1}{900 x ^{2} + 1}) = 1.18

Lösung

x = \frac{1 + sin ( \frac{59}{50} )}{30 1 - sin ( \frac{59}{50} )}, x = - \frac{1 + sin ( \frac{59}{50} )}{30 1 - sin ( \frac{59}{50} )}

Schritte zur Lösung

arcsin (\frac{900 x ^{2} - 1}{900 x ^{2} + 1}) = 1.18

Wende die Eigenschaften der Trigonometrie an

arcsin (\frac{900 x ^{2} - 1}{900 x ^{2} + 1}) = 1.18

arcsin (x) = a \Rightarrow x = sin (a)

\frac{900 x ^{2} - 1}{900 x ^{2} + 1} = sin (1.18)

sin (1.18) = sin (\frac{59}{50})

sin (1.18)

\frac{900 x ^{2} - 1}{900 x ^{2} + 1} = sin (\frac{59}{50})

\frac{900 x ^{2} - 1}{900 x ^{2} + 1} = sin (\frac{59}{50})

Löse

\frac{900 x ^{2} - 1}{900 x ^{2} + 1} = sin (\frac{59}{50}) : x = \frac{1 + sin ( \frac{59}{50} )}{30 1 - sin ( \frac{59}{50} )}, x = - \frac{1 + sin ( \frac{59}{50} )}{30 1 - sin ( \frac{59}{50} )}

\frac{900 x ^{2} - 1}{900 x ^{2} + 1} = sin (\frac{59}{50})

Multipliziere beide Seiten mit

900 x^{2} + 1

\frac{900 x ^{2} - 1}{900 x ^{2} + 1} = sin (\frac{59}{50})

Multipliziere beide Seiten mit

900 x^{2} + 1

\frac{900 x ^{2} - 1}{900 x ^{2} + 1} (900 x^{2} + 1) = sin (\frac{59}{50}) (900 x^{2} + 1)

Vereinfache

900 x^{2} - 1 = sin (\frac{59}{50}) (900 x^{2} + 1)

900 x^{2} - 1 = sin (\frac{59}{50}) (900 x^{2} + 1)

Löse

900 x^{2} - 1 = sin (\frac{59}{50}) (900 x^{2} + 1) : x = \frac{1 + sin ( \frac{59}{50} )}{30 1 - sin ( \frac{59}{50} )}, x = - \frac{1 + sin ( \frac{59}{50} )}{30 1 - sin ( \frac{59}{50} )}

900 x^{2} - 1 = sin (\frac{59}{50}) (900 x^{2} + 1)

Verschiebe

1

auf die rechte Seite

900 x^{2} - 1 = sin (\frac{59}{50}) (900 x^{2} + 1)

Füge

1

zu beiden Seiten hinzu

900 x^{2} - 1 + 1 = sin (\frac{59}{50}) (900 x^{2} + 1) + 1

Vereinfache

900 x^{2} = sin (\frac{59}{50}) (900 x^{2} + 1) + 1

900 x^{2} = sin (\frac{59}{50}) (900 x^{2} + 1) + 1

Verschiebe

sin (\frac{59}{50}) (900 x^{2} + 1)

auf die linke Seite

900 x^{2} = sin (\frac{59}{50}) (900 x^{2} + 1) + 1

Subtrahiere

sin (\frac{59}{50}) (900 x^{2} + 1)

von beiden Seiten

900 x^{2} - sin (\frac{59}{50}) (900 x^{2} + 1) = sin (\frac{59}{50}) (900 x^{2} + 1) + 1 - sin (\frac{59}{50}) (900 x^{2} + 1)

Vereinfache

900 x^{2} - sin (\frac{59}{50}) (900 x^{2} + 1) = 1

900 x^{2} - sin (\frac{59}{50}) (900 x^{2} + 1) = 1

Multipliziere aus

- sin (\frac{59}{50}) (900 x^{2} + 1) : - 900 sin (\frac{59}{50}) x^{2} - sin (\frac{59}{50})

- sin (\frac{59}{50}) (900 x^{2} + 1)

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = - sin (\frac{59}{50}), b = 900 x^{2}, c = 1

= - sin (\frac{59}{50}) \cdot 900 x^{2} + (- sin (\frac{59}{50})) \cdot 1

Wende Minus-Plus Regeln an

+ (- a) = - a

= - 900 sin (\frac{59}{50}) x^{2} - 1 \cdot sin (\frac{59}{50})

Multipliziere:

1 \cdot sin (\frac{59}{50}) = sin (\frac{59}{50})

= - 900 sin (\frac{59}{50}) x^{2} - sin (\frac{59}{50})

900 x^{2} - 900 sin (\frac{59}{50}) x^{2} - sin (\frac{59}{50}) = 1

Verschiebe

sin (\frac{59}{50})

auf die rechte Seite

900 x^{2} - 900 sin (\frac{59}{50}) x^{2} - sin (\frac{59}{50}) = 1

Füge

sin (\frac{59}{50})

zu beiden Seiten hinzu

900 x^{2} - 900 sin (\frac{59}{50}) x^{2} - sin (\frac{59}{50}) + sin (\frac{59}{50}) = 1 + sin (\frac{59}{50})

Vereinfache

900 x^{2} - 900 sin (\frac{59}{50}) x^{2} = 1 + sin (\frac{59}{50})

900 x^{2} - 900 sin (\frac{59}{50}) x^{2} = 1 + sin (\frac{59}{50})

Faktorisiere

900 x^{2} - 900 sin (\frac{59}{50}) x^{2} : 900 (1 - sin (\frac{59}{50})) x^{2}

900 x^{2} - 900 sin (\frac{59}{50}) x^{2}

Schreibe um

= 1 \cdot 900 x^{2} - 900 x^{2} sin (\frac{59}{50})

Klammere gleiche Terme aus

900 x^{2}

= 900 x^{2} (1 - sin (\frac{59}{50}))

900 (1 - sin (\frac{59}{50})) x^{2} = 1 + sin (\frac{59}{50})

Teile beide Seiten durch

900 (1 - sin (\frac{59}{50}))

900 (1 - sin (\frac{59}{50})) x^{2} = 1 + sin (\frac{59}{50})

Teile beide Seiten durch

900 (1 - sin (\frac{59}{50}))

\frac{900 ( 1 - sin ( \frac{59}{50} ) ) x ^{2}}{900 ( 1 - sin ( \frac{59}{50} ) )} = \frac{1}{900 ( 1 - sin ( \frac{59}{50} ) )} + \frac{sin ( \frac{59}{50} )}{900 ( 1 - sin ( \frac{59}{50} ) )}

Vereinfache

\frac{900 ( 1 - sin ( \frac{59}{50} ) ) x ^{2}}{900 ( 1 - sin ( \frac{59}{50} ) )} = \frac{1}{900 ( 1 - sin ( \frac{59}{50} ) )} + \frac{sin ( \frac{59}{50} )}{900 ( 1 - sin ( \frac{59}{50} ) )}

Vereinfache

\frac{900 ( 1 - sin ( \frac{59}{50} ) ) x ^{2}}{900 ( 1 - sin ( \frac{59}{50} ) )} : x^{2}

\frac{900 ( 1 - sin ( \frac{59}{50} ) ) x ^{2}}{900 ( 1 - sin ( \frac{59}{50} ) )}

Teile die Zahlen:

\frac{900}{900} = 1

= \frac{( - sin ( \frac{59}{50} ) + 1 ) x ^{2}}{1 - sin ( \frac{59}{50} )}

Streiche die gemeinsamen Faktoren:

1 - sin (\frac{59}{50})

= x^{2}

Vereinfache

\frac{1}{900 ( 1 - sin ( \frac{59}{50} ) )} + \frac{sin ( \frac{59}{50} )}{900 ( 1 - sin ( \frac{59}{50} ) )} : \frac{1 + sin ( \frac{59}{50} )}{900 ( 1 - sin ( \frac{59}{50} ) )}

\frac{1}{900 ( 1 - sin ( \frac{59}{50} ) )} + \frac{sin ( \frac{59}{50} )}{900 ( 1 - sin ( \frac{59}{50} ) )}

Da die Nenner gleich sind, fasse die Brüche zusammen.:

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

= \frac{1 + sin ( \frac{59}{50} )}{900 ( 1 - sin ( \frac{59}{50} ) )}

x^{2} = \frac{1 + sin ( \frac{59}{50} )}{900 ( 1 - sin ( \frac{59}{50} ) )}

x^{2} = \frac{1 + sin ( \frac{59}{50} )}{900 ( 1 - sin ( \frac{59}{50} ) )}

x^{2} = \frac{1 + sin ( \frac{59}{50} )}{900 ( 1 - sin ( \frac{59}{50} ) )}

Für

x^{2} = f (a)

sind die Lösungen

x = f (a), - f (a)

x = \frac{1 + sin ( \frac{59}{50} )}{900 ( 1 - sin ( \frac{59}{50} ) )}, x = - \frac{1 + sin ( \frac{59}{50} )}{900 ( 1 - sin ( \frac{59}{50} ) )}

\frac{1 + sin ( \frac{59}{50} )}{900 ( 1 - sin ( \frac{59}{50} ) )} = \frac{1 + sin ( \frac{59}{50} )}{30 1 - sin ( \frac{59}{50} )}

\frac{1 + sin ( \frac{59}{50} )}{900 ( 1 - sin ( \frac{59}{50} ) )}

Wende Radikal Regel an:

n \frac{a}{b} = \frac{n a}{n b},

angenommen

a \geq 0, b \geq 0

= \frac{1 + sin ( \frac{59}{50} )}{900 ( - sin ( \frac{59}{50} ) + 1 )}

Wende Radikal Regel an:

n ab = n a n b,

angenommen

a \geq 0, b \geq 0

900 (- sin (\frac{59}{50}) + 1) = 900 - sin (\frac{59}{50}) + 1

= \frac{1 + sin ( \frac{59}{50} )}{900 - sin ( \frac{59}{50} ) + 1}

900 = 30

900

Faktorisiere die Zahl:

900 = 3 0^{2}

= 3 0^{2}

Wende Radikal Regel an:

n a^{n} = a

3 0^{2} = 30

= 30

= \frac{1 + sin ( \frac{59}{50} )}{30 - sin ( \frac{59}{50} ) + 1}

= \frac{1 + sin ( \frac{59}{50} )}{30 1 - sin ( \frac{59}{50} )}

- \frac{1 + sin ( \frac{59}{50} )}{900 ( 1 - sin ( \frac{59}{50} ) )} = - \frac{1 + sin ( \frac{59}{50} )}{30 1 - sin ( \frac{59}{50} )}

- \frac{1 + sin ( \frac{59}{50} )}{900 ( 1 - sin ( \frac{59}{50} ) )}

Vereinfache

\frac{1 + sin ( \frac{59}{50} )}{900 ( 1 - sin ( \frac{59}{50} ) )} : \frac{1 + sin ( \frac{59}{50} )}{30 - sin ( \frac{59}{50} ) + 1}

\frac{1 + sin ( \frac{59}{50} )}{900 ( 1 - sin ( \frac{59}{50} ) )}

Wende Radikal Regel an:

n \frac{a}{b} = \frac{n a}{n b},

angenommen

a \geq 0, b \geq 0

= \frac{1 + sin ( \frac{59}{50} )}{900 ( - sin ( \frac{59}{50} ) + 1 )}

Wende Radikal Regel an:

n ab = n a n b,

angenommen

a \geq 0, b \geq 0

900 (- sin (\frac{59}{50}) + 1) = 900 - sin (\frac{59}{50}) + 1

= \frac{1 + sin ( \frac{59}{50} )}{900 - sin ( \frac{59}{50} ) + 1}

900 = 30

900

Faktorisiere die Zahl:

900 = 3 0^{2}

= 3 0^{2}

Wende Radikal Regel an:

n a^{n} = a

3 0^{2} = 30

= 30

= \frac{1 + sin ( \frac{59}{50} )}{30 - sin ( \frac{59}{50} ) + 1}

= - \frac{sin ( \frac{59}{50} ) + 1}{30 - sin ( \frac{59}{50} ) + 1}

= - \frac{1 + sin ( \frac{59}{50} )}{30 1 - sin ( \frac{59}{50} )}

x = \frac{1 + sin ( \frac{59}{50} )}{30 1 - sin ( \frac{59}{50} )}, x = - \frac{1 + sin ( \frac{59}{50} )}{30 1 - sin ( \frac{59}{50} )}

x = \frac{1 + sin ( \frac{59}{50} )}{30 1 - sin ( \frac{59}{50} )}, x = - \frac{1 + sin ( \frac{59}{50} )}{30 1 - sin ( \frac{59}{50} )}

x = \frac{1 + sin ( \frac{59}{50} )}{30 1 - sin ( \frac{59}{50} )}, x = - \frac{1 + sin ( \frac{59}{50} )}{30 1 - sin ( \frac{59}{50} )}

Graph

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