es

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(x)cos(x)=3cos(x)

Solución

sin (x) cos (x) = 3 cos (x)

Solución

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

+1

Grados

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

Pasos de solución

sin (x) cos (x) = 3 cos (x)

Restar

3 cos (x)

de ambos lados

sin (x) cos (x) - 3 cos (x) = 0

Factorizar

sin (x) cos (x) - 3 cos (x) : cos (x) (sin (x) - 3)

sin (x) cos (x) - 3 cos (x)

Factorizar el termino común

cos (x)

= cos (x) (sin (x) - 3)

cos (x) (sin (x) - 3) = 0

Resolver cada parte por separado

cos (x) = 0 or sin (x) - 3 = 0

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = 0

Soluciones generales para

cos (x) = 0

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 = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

sin (x) - 3 = 0 :

Sin solución

sin (x) - 3 = 0

Mover

3

al lado derecho

sin (x) - 3 = 0

Sumar

3

a ambos lados

sin (x) - 3 + 3 = 0 + 3

Simplificar

sin (x) = 3

sin (x) = 3

- 1 \leq sin (x) \leq 1

Sin soluci \overset{o}{ˊ} n

Combinar toda las soluciones

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Ejemplos populares

sin (π x) = 0

csc(x-pi)cos^2(x-pi)-cot(x-pi)=0

csc (x - π) cos^{2} (x - π) - cot (x - π) = 0

tan^2(θ)+6tan(θ)+8=0

tan^{2} (θ) + 6 tan (θ) + 8 = 0

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

sin (\frac{x}{2}) + cos (x) = 1

-cos(x)+cos(2x)=0

- cos (x) + cos (2 x) = 0