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solvefor t,(rcos(t))/r r>0

Solución

resolver para

t, \frac{r cos ( t )}{r} r > 0

- \frac{π}{2} + 2 πn < t < \frac{π}{2} + 2 πn

Pasos de solución

\frac{r cos ( t )}{r} r > 0

Multiplicar fracciones:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

\frac{r cos ( t ) r}{r} > 0

Eliminar los terminos comunes:

r

r cos (t) > 0

Dividir ambos lados entre

r

r cos (t) > 0

Dividir ambos lados entre

r

\frac{r cos ( t )}{r} > \frac{0}{r}

Simplificar

cos (t) > 0

cos (t) > 0

Para

cos (x) > a

, si

- 1 \leq a < 1

entonces

- arccos (a) + 2 πn < x < arccos (a) + 2 πn

- arccos (0) + 2 πn < t < arccos (0) + 2 πn

Simplificar

- arccos (0) : - \frac{π}{2}

- arccos (0)

Utilizar la siguiente identidad trivial:

arccos (0) = \frac{π}{2}

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= - \frac{π}{2}

Simplificar

arccos (0) : \frac{π}{2}

arccos (0)

Utilizar la siguiente identidad trivial:

arccos (0) = \frac{π}{2}

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= \frac{π}{2}

- \frac{π}{2} + 2 πn < t < \frac{π}{2} + 2 πn

cos (\frac{4}{3} x + \frac{π}{6}) \geq 1

2 - 2 cos (a) \geq 0

sin (x) cos (x) > 0

cos (x) + sin (x) > 0

2 cos (2 x) < 1