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Popular >

0.5cos(x)=cos(x)

Solución

0.5 cos (x) = cos (x)

Solución

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

Grados

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

Pasos de solución

0.5 cos (x) = cos (x)

Usando el método de sustitución

0.5 cos (x) = cos (x)

Sea:

cos (x) = u

0.5 u = u

0.5 u = u : u = 0

0.5 u = u

Multiplicar ambos lados por

10

0.5 u = u

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

0.5 u \cdot 10 = u \cdot 10

Simplificar

5 u = u \cdot 10

5 u = u \cdot 10

Mover

u 10

al lado izquierdo

5 u = u \cdot 10

Restar

u 10

de ambos lados

5 u - u \cdot 10 = u \cdot 10 - u \cdot 10

Simplificar

- 5 u = 0

- 5 u = 0

Dividir ambos lados entre

- 5

- 5 u = 0

Dividir ambos lados entre

- 5

\frac{- 5 u}{- 5} = \frac{0}{- 5}

Simplificar

u = 0

u = 0

Sustituir en la ecuación

u = cos (x)

cos (x) = 0

cos (x) = 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

Combinar toda las soluciones

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

Ejemplos populares

tan(a)=-1/2

tan (a) = - \frac{1}{2}

sin(2x+30)=-(sqrt(3))/2

sin (2 x + 3 0^{\circ}) = - \frac{3}{2}

8tan^2(θ)-1=7tan(θ)

8 tan^{2} (θ) - 1 = 7 tan (θ)

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

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

sin(x+pi/4)=1

sin (x + \frac{π}{4}) = 1