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Beliebt Trigonometrie >

sin(x+20)*csc(70)=1

Lösung

sin (x + 2 0^{\circ}) \cdot csc (7 0^{\circ}) = 1

Lösung

x = 1.22173 \dots + 36 0^{\circ} n - 2 0^{\circ}, x = 18 0^{\circ} - 1.22173 \dots + 36 0^{\circ} n - 2 0^{\circ}

+1

Radianten

x = 1.22173 \dots - \frac{π}{9} + 2 πn, x = π - 1.22173 \dots - \frac{π}{9} + 2 πn

Schritte zur Lösung

sin (x + 2 0^{\circ}) csc (7 0^{\circ}) = 1

Teile beide Seiten durch

csc (7 0^{\circ})

sin (x + 2 0^{\circ}) csc (7 0^{\circ}) = 1

Teile beide Seiten durch

csc (7 0^{\circ})

\frac{sin ( x + 2 0 ^{\circ} ) csc ( 7 0 ^{\circ} )}{csc ( 7 0 ^{\circ} )} = \frac{1}{csc ( 7 0 ^{\circ} )}

Vereinfache

sin (x + 2 0^{\circ}) = \frac{1}{csc ( 7 0 ^{\circ} )}

sin (x + 2 0^{\circ}) = \frac{1}{csc ( 7 0 ^{\circ} )}

Wende die Eigenschaften der Trigonometrie an

sin (x + 2 0^{\circ}) = \frac{1}{csc ( 7 0 ^{\circ} )}

Allgemeine Lösung für

sin (x + 2 0^{\circ}) = \frac{1}{csc ( 7 0 ^{\circ} )}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x + 2 0^{\circ} = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n, x + 2 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n

x + 2 0^{\circ} = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n, x + 2 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n

Löse

x + 2 0^{\circ} = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n : x = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

x + 2 0^{\circ} = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n

Verschiebe

2 0^{\circ}

auf die rechte Seite

x + 2 0^{\circ} = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n

Subtrahiere

2 0^{\circ}

von beiden Seiten

x + 2 0^{\circ} - 2 0^{\circ} = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

Vereinfache

x = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

x = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

Löse

x + 2 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n : x = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

x + 2 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n

Verschiebe

2 0^{\circ}

auf die rechte Seite

x + 2 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n

Subtrahiere

2 0^{\circ}

von beiden Seiten

x + 2 0^{\circ} - 2 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

Vereinfache

x = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

x = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

x = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}, x = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

Zeige Lösungen in Dezimalform

x = 1.22173 \dots + 36 0^{\circ} n - 2 0^{\circ}, x = 18 0^{\circ} - 1.22173 \dots + 36 0^{\circ} n - 2 0^{\circ}

Graph

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