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Popular >

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

Solución

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

Solución

x = 2 πn

+1

Grados

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

Pasos de solución

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

Re-escribir usando identidades trigonométricas

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

Utilizar la identidad pitagórica:

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

= cos (x) + 1

cos (x) + 1 = 2

Mover

1

al lado derecho

cos (x) + 1 = 2

Restar

1

de ambos lados

cos (x) + 1 - 1 = 2 - 1

Simplificar

cos (x) = 1

cos (x) = 1

Soluciones generales para

cos (x) = 1

cos (x)

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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = 0 + 2 πn

x = 0 + 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

Ejemplos populares

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sin (135 - x) = sin (x)

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4cos^2(x)-8cos(x)+3=0

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sin (2 x) = - 0.6