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Beliebt Trigonometrie >

sin(90-θ)=0.5745

Lösung

sin (9 0^{\circ} - θ) = 0.5745

Lösung

θ = - 36 0^{\circ} n + 9 0^{\circ} - 0.61199 \dots, θ = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + 0.61199 \dots

Radianten

θ = \frac{π}{2} - 0.61199 \dots - 2 πn, θ = - π + \frac{π}{2} + 0.61199 \dots - 2 πn

Schritte zur Lösung

sin (9 0^{\circ} - θ) = 0.5745

Wende die Eigenschaften der Trigonometrie an

sin (9 0^{\circ} - θ) = 0.5745

Allgemeine Lösung für

sin (9 0^{\circ} - θ) = 0.5745

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

9 0^{\circ} - θ = arcsin (0.5745) + 36 0^{\circ} n, 9 0^{\circ} - θ = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n

9 0^{\circ} - θ = arcsin (0.5745) + 36 0^{\circ} n, 9 0^{\circ} - θ = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n

Löse

9 0^{\circ} - θ = arcsin (0.5745) + 36 0^{\circ} n : θ = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (0.5745)

9 0^{\circ} - θ = arcsin (0.5745) + 36 0^{\circ} n

Verschiebe

9 0^{\circ}

auf die rechte Seite

9 0^{\circ} - θ = arcsin (0.5745) + 36 0^{\circ} n

Subtrahiere

9 0^{\circ}

von beiden Seiten

9 0^{\circ} - θ - 9 0^{\circ} = arcsin (0.5745) + 36 0^{\circ} n - 9 0^{\circ}

Vereinfache

- θ = arcsin (0.5745) + 36 0^{\circ} n - 9 0^{\circ}

- θ = arcsin (0.5745) + 36 0^{\circ} n - 9 0^{\circ}

Teile beide Seiten durch

- 1

- θ = arcsin (0.5745) + 36 0^{\circ} n - 9 0^{\circ}

Teile beide Seiten durch

- 1

\frac{- θ}{- 1} = \frac{arcsin ( 0.5745 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

Vereinfache

\frac{- θ}{- 1} = \frac{arcsin ( 0.5745 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

Vereinfache

\frac{- θ}{- 1} : θ

\frac{- θ}{- 1}

Wende Bruchregel an:

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

= \frac{θ}{1}

Wende Regel an

\frac{a}{1} = a

= θ

Vereinfache

\frac{arcsin ( 0.5745 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} : - 36 0^{\circ} n + 9 0^{\circ} - arcsin (0.5745)

\frac{arcsin ( 0.5745 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

Fasse gleiche Terme zusammen

= \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} + \frac{arcsin ( 0.5745 )}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

Wende Bruchregel an:

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

= - \frac{36 0 ^{\circ} n}{1}

Wende Regel an

\frac{a}{1} = a

= - 36 0^{\circ} n

= - 36 0^{\circ} n - \frac{9 0 ^{\circ}}{- 1} + \frac{arcsin ( 0.5745 )}{- 1}

\frac{9 0 ^{\circ}}{- 1} = - 9 0^{\circ}

\frac{9 0 ^{\circ}}{- 1}

Wende Bruchregel an:

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

= - \frac{9 0 ^{\circ}}{1}

Wende Bruchregel an:

\frac{a}{1} = a

\frac{9 0 ^{\circ}}{1} = 9 0^{\circ}

= - 9 0^{\circ}

\frac{arcsin ( 0.5745 )}{- 1} = - arcsin (0.5745)

\frac{arcsin ( 0.5745 )}{- 1}

Wende Bruchregel an:

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

= - \frac{arcsin ( 0.5745 )}{1}

Wende Regel an

\frac{a}{1} = a

= - arcsin (0.5745)

= - 36 0^{\circ} n - (- 9 0^{\circ}) - arcsin (0.5745)

Wende Regel an

- (- a) = a

= - 36 0^{\circ} n + 9 0^{\circ} - arcsin (0.5745)

θ = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (0.5745)

θ = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (0.5745)

θ = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (0.5745)

Löse

9 0^{\circ} - θ = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n : θ = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (0.5745)

9 0^{\circ} - θ = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n

Verschiebe

9 0^{\circ}

auf die rechte Seite

9 0^{\circ} - θ = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n

Subtrahiere

9 0^{\circ}

von beiden Seiten

9 0^{\circ} - θ - 9 0^{\circ} = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n - 9 0^{\circ}

Vereinfache

- θ = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n - 9 0^{\circ}

- θ = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n - 9 0^{\circ}

Teile beide Seiten durch

- 1

- θ = 18 0^{\circ} - arcsin (0.5745) + 36 0^{\circ} n - 9 0^{\circ}

Teile beide Seiten durch

- 1

\frac{- θ}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.5745 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

Vereinfache

\frac{- θ}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.5745 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

Vereinfache

\frac{- θ}{- 1} : θ

\frac{- θ}{- 1}

Wende Bruchregel an:

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

= \frac{θ}{1}

Wende Regel an

\frac{a}{1} = a

= θ

Vereinfache

\frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.5745 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} : - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (0.5745)

\frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.5745 )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

Fasse gleiche Terme zusammen

= \frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.5745 )}{- 1}

\frac{18 0 ^{\circ}}{- 1} = - 18 0^{\circ}

\frac{18 0 ^{\circ}}{- 1}

Wende Bruchregel an:

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

= - 18 0^{\circ}

Wende Regel an

\frac{a}{1} = a

= - 18 0^{\circ}

= - 18 0^{\circ} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.5745 )}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

Wende Bruchregel an:

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

= - \frac{36 0 ^{\circ} n}{1}

Wende Regel an

\frac{a}{1} = a

= - 36 0^{\circ} n

= - 18 0^{\circ} - 36 0^{\circ} n - \frac{9 0 ^{\circ}}{- 1} - \frac{arcsin ( 0.5745 )}{- 1}

\frac{9 0 ^{\circ}}{- 1} = - 9 0^{\circ}

\frac{9 0 ^{\circ}}{- 1}

Wende Bruchregel an:

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

= - \frac{9 0 ^{\circ}}{1}

Wende Bruchregel an:

\frac{a}{1} = a

\frac{9 0 ^{\circ}}{1} = 9 0^{\circ}

= - 9 0^{\circ}

\frac{arcsin ( 0.5745 )}{- 1} = - arcsin (0.5745)

\frac{arcsin ( 0.5745 )}{- 1}

Wende Bruchregel an:

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

= - \frac{arcsin ( 0.5745 )}{1}

Wende Regel an

\frac{a}{1} = a

= - arcsin (0.5745)

= - 18 0^{\circ} - 36 0^{\circ} n - (- 9 0^{\circ}) - (- arcsin (0.5745))

Wende Regel an

- (- a) = a

= - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (0.5745)

θ = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (0.5745)

θ = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (0.5745)

θ = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (0.5745)

θ = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (0.5745), θ = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (0.5745)

Zeige Lösungen in Dezimalform

θ = - 36 0^{\circ} n + 9 0^{\circ} - 0.61199 \dots, θ = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + 0.61199 \dots

Graph

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