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Popular Trigonometría >

solvefor t,16sin(t)cos(t)=6sin(t)

Solución

resolver para

t, 16 sin (t) cos (t) = 6 sin (t)

Solución

t = 2 πn, t = π + 2 πn, t = 1.18639 \dots + 2 πn, t = 2 π - 1.18639 \dots + 2 πn

+1

Grados

t = 0^{\circ} + 36 0^{\circ} n, t = 18 0^{\circ} + 36 0^{\circ} n, t = 67.97568 \dots^{\circ} + 36 0^{\circ} n, t = 292.02431 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

16 sin (t) cos (t) = 6 sin (t)

Restar

6 sin (t)

de ambos lados

16 sin (t) cos (t) - 6 sin (t) = 0

Factorizar

16 sin (t) cos (t) - 6 sin (t) : 2 sin (t) (8 cos (t) - 3)

16 sin (t) cos (t) - 6 sin (t)

Reescribir

- 6

como

3 \cdot 2

Reescribir

16

como

8 \cdot 2

= 8 \cdot 2 sin (t) cos (t) + 3 \cdot 2 sin (t)

Factorizar el termino común

2 sin (t)

= 2 sin (t) (8 cos (t) - 3)

2 sin (t) (8 cos (t) - 3) = 0

Resolver cada parte por separado

sin (t) = 0 or 8 cos (t) - 3 = 0

sin (t) = 0 : t = 2 πn, t = π + 2 πn

sin (t) = 0

Soluciones generales para

sin (t) = 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}

t = 0 + 2 πn, t = π + 2 πn

t = 0 + 2 πn, t = π + 2 πn

Resolver

t = 0 + 2 πn : t = 2 πn

t = 0 + 2 πn

0 + 2 πn = 2 πn

t = 2 πn

t = 2 πn, t = π + 2 πn

8 cos (t) - 3 = 0 : t = arccos (\frac{3}{8}) + 2 πn, t = 2 π - arccos (\frac{3}{8}) + 2 πn

8 cos (t) - 3 = 0

Desplace

3

a la derecha

8 cos (t) - 3 = 0

Sumar

3

a ambos lados

8 cos (t) - 3 + 3 = 0 + 3

Simplificar

8 cos (t) = 3

8 cos (t) = 3

Dividir ambos lados entre

8

8 cos (t) = 3

Dividir ambos lados entre

8

\frac{8 cos ( t )}{8} = \frac{3}{8}

Simplificar

cos (t) = \frac{3}{8}

cos (t) = \frac{3}{8}

Aplicar propiedades trigonométricas inversas

cos (t) = \frac{3}{8}

Soluciones generales para

cos (t) = \frac{3}{8}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

t = arccos (\frac{3}{8}) + 2 πn, t = 2 π - arccos (\frac{3}{8}) + 2 πn

t = arccos (\frac{3}{8}) + 2 πn, t = 2 π - arccos (\frac{3}{8}) + 2 πn

Combinar toda las soluciones

t = 2 πn, t = π + 2 πn, t = arccos (\frac{3}{8}) + 2 πn, t = 2 π - arccos (\frac{3}{8}) + 2 πn

Mostrar soluciones en forma decimal

t = 2 πn, t = π + 2 πn, t = 1.18639 \dots + 2 πn, t = 2 π - 1.18639 \dots + 2 πn

Gráfica

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