e^{sin(x)}=2

Lösung

e^{s i n (x)} = 2

x = 0.76584 \dots + 2 πn, x = π - 0.76584 \dots + 2 πn

Grad

x = 43.87975 \dots^{\circ} + 36 0^{\circ} n, x = 136.12024 \dots^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

e^{s i n (x)} = 2

Wende Exponentenregel an

e^{s i n (x)} = 2

Wenn

f (x) = g (x)

, dann

ln (f (x)) = ln (g (x))

ln (e^{s i n (x)}) = ln (2)

Wende die log Regel an:

ln (e^{a}) = a

ln (e^{s i n (x)}) = sin (x)

sin (x) = ln (2)

sin (x) = ln (2)

Wende die Eigenschaften der Trigonometrie an

sin (x) = ln (2)

Allgemeine Lösung für

sin (x) = ln (2)

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (ln (2)) + 2 πn, x = π - arcsin (ln (2)) + 2 πn

x = arcsin (ln (2)) + 2 πn, x = π - arcsin (ln (2)) + 2 πn

Zeige Lösungen in Dezimalform

x = 0.76584 \dots + 2 πn, x = π - 0.76584 \dots + 2 πn

\frac{sec ( x )}{cot ( x ) tan ( x )} = sin (x)

\frac{cos ( x )}{2} = - 1

4 sin (θ) + 23 = 0

400 + 290 cos (x) + 290 sin (x) = 0

2 = 2 sin (2 θ)