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Beliebt Trigonometrie >

cos(5a+40)= 3/5

Lösung

cos (5 a + 4 0^{\circ}) = \frac{3}{5}

Lösung

a = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{0.92729 \dots}{5}, a = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{0.92729 \dots}{5}

Radianten

a = - \frac{2 π}{45} + \frac{0.92729 \dots}{5} + \frac{2 π}{5} n, a = \frac{2 π}{5} - \frac{2 π}{45} - \frac{0.92729 \dots}{5} + \frac{2 π}{5} n

Schritte zur Lösung

cos (5 a + 4 0^{\circ}) = \frac{3}{5}

Wende die Eigenschaften der Trigonometrie an

cos (5 a + 4 0^{\circ}) = \frac{3}{5}

Allgemeine Lösung für

cos (5 a + 4 0^{\circ}) = \frac{3}{5}

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

5 a + 4 0^{\circ} = arccos (\frac{3}{5}) + 36 0^{\circ} n, 5 a + 4 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n

5 a + 4 0^{\circ} = arccos (\frac{3}{5}) + 36 0^{\circ} n, 5 a + 4 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n

Löse

5 a + 4 0^{\circ} = arccos (\frac{3}{5}) + 36 0^{\circ} n : a = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

5 a + 4 0^{\circ} = arccos (\frac{3}{5}) + 36 0^{\circ} n

Verschiebe

4 0^{\circ}

auf die rechte Seite

5 a + 4 0^{\circ} = arccos (\frac{3}{5}) + 36 0^{\circ} n

Subtrahiere

4 0^{\circ}

von beiden Seiten

5 a + 4 0^{\circ} - 4 0^{\circ} = arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

Vereinfache

5 a = arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

5 a = arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

Teile beide Seiten durch

5

5 a = arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

Teile beide Seiten durch

5

\frac{5 a}{5} = \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

Vereinfache

\frac{5 a}{5} = \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

Vereinfache

\frac{5 a}{5} : a

\frac{5 a}{5}

Teile die Zahlen:

\frac{5}{5} = 1

= a

Vereinfache

\frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5} : \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

\frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

Fasse gleiche Terme zusammen

= \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5} + \frac{arccos ( \frac{3}{5} )}{5}

\frac{4 0 ^{\circ}}{5} = 8^{\circ}

\frac{4 0 ^{\circ}}{5}

Wende Bruchregel an:

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

= \frac{36 0 ^{\circ}}{9 \cdot 5}

Multipliziere die Zahlen:

9 \cdot 5 = 45

= 8^{\circ}

= \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

a = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

a = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

a = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

Löse

5 a + 4 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n : a = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

5 a + 4 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n

Verschiebe

4 0^{\circ}

auf die rechte Seite

5 a + 4 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n

Subtrahiere

4 0^{\circ}

von beiden Seiten

5 a + 4 0^{\circ} - 4 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

Vereinfache

5 a = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

5 a = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

Teile beide Seiten durch

5

5 a = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

Teile beide Seiten durch

5

\frac{5 a}{5} = 7 2^{\circ} - \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

Vereinfache

\frac{5 a}{5} = 7 2^{\circ} - \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

Vereinfache

\frac{5 a}{5} : a

\frac{5 a}{5}

Teile die Zahlen:

\frac{5}{5} = 1

= a

Vereinfache

7 2^{\circ} - \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5} : 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

7 2^{\circ} - \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

Fasse gleiche Terme zusammen

= 7 2^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5} - \frac{arccos ( \frac{3}{5} )}{5}

\frac{4 0 ^{\circ}}{5} = 8^{\circ}

\frac{4 0 ^{\circ}}{5}

Wende Bruchregel an:

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

= \frac{36 0 ^{\circ}}{9 \cdot 5}

Multipliziere die Zahlen:

9 \cdot 5 = 45

= 8^{\circ}

= 7 2^{\circ} + \frac{36 0 ^{\circ} n}{5} - 8^{\circ} - \frac{arccos ( \frac{3}{5} )}{5}

Fasse gleiche Terme zusammen

= 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

a = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

a = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

a = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

a = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}, a = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

Zeige Lösungen in Dezimalform

a = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{0.92729 \dots}{5}, a = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{0.92729 \dots}{5}

Graph

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