sin(α)= 3/5

Lösung

sin (α) = \frac{3}{5}

α = 0.64350 \dots + 2 πn, α = π - 0.64350 \dots + 2 πn

Grad

α = 36.86989 \dots^{\circ} + 36 0^{\circ} n, α = 143.13010 \dots^{\circ} + 36 0^{\circ} n

Schritte zur Lösung

sin (α) = \frac{3}{5}

Wende die Eigenschaften der Trigonometrie an

sin (α) = \frac{3}{5}

Allgemeine Lösung für

sin (α) = \frac{3}{5}

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

α = arcsin (\frac{3}{5}) + 2 πn, α = π - arcsin (\frac{3}{5}) + 2 πn

α = arcsin (\frac{3}{5}) + 2 πn, α = π - arcsin (\frac{3}{5}) + 2 πn

Zeige Lösungen in Dezimalform

α = 0.64350 \dots + 2 πn, α = π - 0.64350 \dots + 2 πn

so l v e f or x, tan^{2} (x) = 2

so l v e f or x, \frac{p}{q} = sin^{2} (x)

cos (2 x) = 1 - 2 (\frac{3}{5})^{2}

4 sin^{2} (x) = 5 - 4 cos (x), 0 \leq x < 2 π

cos (θ) = \frac{3}{4}