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Populaire >

sin^2(θ)=0.4567

Solution

sin^{2} (θ) = 0.4567

θ = 0.74204 \dots + 2 πn, θ = π - 0.74204 \dots + 2 πn, θ = - 0.74204 \dots + 2 πn, θ = π + 0.74204 \dots + 2 πn

Degrés

θ = 42.51598 \dots^{\circ} + 36 0^{\circ} n, θ = 137.48401 \dots^{\circ} + 36 0^{\circ} n, θ = - 42.51598 \dots^{\circ} + 36 0^{\circ} n, θ = 222.51598 \dots^{\circ} + 36 0^{\circ} n

étapes des solutions

sin^{2} (θ) = 0.4567

Résoudre par substitution

sin^{2} (θ) = 0.4567

Soit :

sin (θ) = u

u^{2} = 0.4567

u^{2} = 0.4567 : u = 0.4567, u = - 0.4567

u^{2} = 0.4567

Pour

x^{2} = f (a)

les solutions sont

x = f (a), - f (a)

u = 0.4567, u = - 0.4567

Remplacer

u = sin (θ)

sin (θ) = 0.4567, sin (θ) = - 0.4567

sin (θ) = 0.4567, sin (θ) = - 0.4567

sin (θ) = 0.4567 : θ = arcsin (0.4567) + 2 πn, θ = π - arcsin (0.4567) + 2 πn

sin (θ) = 0.4567

Appliquer les propriétés trigonométriques inverses

sin (θ) = 0.4567

Solutions générales pour

sin (θ) = 0.4567

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

θ = arcsin (0.4567) + 2 πn, θ = π - arcsin (0.4567) + 2 πn

θ = arcsin (0.4567) + 2 πn, θ = π - arcsin (0.4567) + 2 πn

sin (θ) = - 0.4567 : θ = arcsin (- 0.4567) + 2 πn, θ = π + arcsin (0.4567) + 2 πn

sin (θ) = - 0.4567

Appliquer les propriétés trigonométriques inverses

sin (θ) = - 0.4567

Solutions générales pour

sin (θ) = - 0.4567

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

θ = arcsin (- 0.4567) + 2 πn, θ = π + arcsin (0.4567) + 2 πn

θ = arcsin (- 0.4567) + 2 πn, θ = π + arcsin (0.4567) + 2 πn

Combiner toutes les solutions

θ = arcsin (0.4567) + 2 πn, θ = π - arcsin (0.4567) + 2 πn, θ = arcsin (- 0.4567) + 2 πn, θ = π + arcsin (0.4567) + 2 πn

Montrer les solutions sous la forme décimale

θ = 0.74204 \dots + 2 πn, θ = π - 0.74204 \dots + 2 πn, θ = - 0.74204 \dots + 2 πn, θ = π + 0.74204 \dots + 2 πn

\frac{sin ( A )}{cos ( A )} - 2 = 1

cos (θ) = \frac{10}{15}

sin (θ) = \frac{40}{60}

10 = 3.44 sin (0.51 t + 4.11) + 9.48

2 cot^{2} (z) + 5 = 7 csc (z)