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2sin^2(x)+sin^2(x)+cos^2(x)=1

Solución

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

x = 2 πn, x = π + 2 πn

Grados

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

Pasos de solución

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

Re-escribir usando identidades trigonométricas

2 sin^{2} (x) + sin^{2} (x) + cos^{2} (x)

Utilizar la identidad pitagórica:

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

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

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

Mover

1

al lado derecho

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

Restar

1

de ambos lados

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

Simplificar

2 sin^{2} (x) = 0

2 sin^{2} (x) = 0

Dividir ambos lados entre

2

2 sin^{2} (x) = 0

Dividir ambos lados entre

2

2 sin^{2} (x) = 0

Dividir ambos lados entre

2

\frac{2 sin ^{2} ( x )}{2} = \frac{0}{2}

Simplificar

sin^{2} (x) = 0

sin^{2} (x) = 0

Aplicar la regla

x^{n} = 0 \Rightarrow x = 0

sin (x) = 0

Soluciones generales para

sin (x) = 0

tabla de valores periódicos con

2 πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Resolver

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

sin^{2} (x) + 3 cos (x) - 1 = 0

cos (\frac{3 x - 7}{2}) = 0

3 tan^{2} (x) = \frac{8}{sin ^{2} ( x )}

sin^{2} (x) + sin^{22} (x) + sin^{23} (x) = 1

5 sin (1.75 x) = 1.4