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Populaire >

sin^2(x)+0.49=1

Solution

sin^{2} (x) + 0.49 = 1

x = 0.79539 \dots + 2 πn, x = π - 0.79539 \dots + 2 πn, x = - 0.79539 \dots + 2 πn, x = π + 0.79539 \dots + 2 πn

Degrés

x = 45.57299 \dots^{\circ} + 36 0^{\circ} n, x = 134.42700 \dots^{\circ} + 36 0^{\circ} n, x = - 45.57299 \dots^{\circ} + 36 0^{\circ} n, x = 225.57299 \dots^{\circ} + 36 0^{\circ} n

étapes des solutions

sin^{2} (x) + 0.49 = 1

Résoudre par substitution

sin^{2} (x) + 0.49 = 1

Soit :

sin (x) = u

u^{2} + 0.49 = 1

u^{2} + 0.49 = 1 : u = 0.51, u = - 0.51

u^{2} + 0.49 = 1

Déplacer

0.49

vers la droite

u^{2} + 0.49 = 1

Soustraire

0.49

des deux côtés

u^{2} + 0.49 - 0.49 = 1 - 0.49

Simplifier

u^{2} = 0.51

u^{2} = 0.51

Pour

x^{2} = f (a)

les solutions sont

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

u = 0.51, u = - 0.51

Remplacer

u = sin (x)

sin (x) = 0.51, sin (x) = - 0.51

sin (x) = 0.51, sin (x) = - 0.51

sin (x) = 0.51 : x = arcsin (0.51) + 2 πn, x = π - arcsin (0.51) + 2 πn

sin (x) = 0.51

Appliquer les propriétés trigonométriques inverses

sin (x) = 0.51

Solutions générales pour

sin (x) = 0.51

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

x = arcsin (0.51) + 2 πn, x = π - arcsin (0.51) + 2 πn

x = arcsin (0.51) + 2 πn, x = π - arcsin (0.51) + 2 πn

sin (x) = - 0.51 : x = arcsin (- 0.51) + 2 πn, x = π + arcsin (0.51) + 2 πn

sin (x) = - 0.51

Appliquer les propriétés trigonométriques inverses

sin (x) = - 0.51

Solutions générales pour

sin (x) = - 0.51

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

x = arcsin (- 0.51) + 2 πn, x = π + arcsin (0.51) + 2 πn

x = arcsin (- 0.51) + 2 πn, x = π + arcsin (0.51) + 2 πn

Combiner toutes les solutions

x = arcsin (0.51) + 2 πn, x = π - arcsin (0.51) + 2 πn, x = arcsin (- 0.51) + 2 πn, x = π + arcsin (0.51) + 2 πn

Montrer les solutions sous la forme décimale

x = 0.79539 \dots + 2 πn, x = π - 0.79539 \dots + 2 πn, x = - 0.79539 \dots + 2 πn, x = π + 0.79539 \dots + 2 πn

6 cos^{2} (θ) + sin^{2} (θ) = 4

15 sin (3 0^{\circ}) = 10 sin (x)

sin (0) = - sin (o) cos (0)

\frac{sin ( 78.0538888 9 ^{\circ} )}{8} = \frac{sin ( x )}{10}

sin (x) = 32