Question

3- Calcule o valor de y:
a) y = sen (30°). cos(120°) + cos(30°).sen(120°)
b) y = sen (0°). cos(210°) + cos(0°).sen(210°) c) y = tg(225°). cos(150°) + sen(150°).tg (225°)
d) y = tg (57) .tg (7) + tg ().tg (S)​

Answer 1

$\Large\boxed{\begin{array}{l}\rm a)\\\sf y=sen(30^\circ)\cdot cos(120^\circ)+cos(30^\circ)\cdot sen(120^\circ)\\\sf y=sen(30^\circ+120^\circ)=sen(150^\circ)\\\sf y= sen(30^\circ)=\dfrac{1}{2}\\\\\rm b)\\\sf y=sen(0^\circ)\cdot cos(210^\circ) + cos(0^\circ)\cdot sen(210^\circ)\\\sf y= sen(0+210^\circ)=sen(210^\circ)=-sen(30^\circ)\\\sf y=-\dfrac{1}{2}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm c)\\\sf y= tg(225^\circ)\cdot cos(150^\circ)+sen(150^\circ)\cdot tg(225^\circ)\\\\\sf y= 1\cdot\bigg(-\dfrac{\sqrt{3}}{2}\bigg)+\dfrac{1}{2}\cdot1\\\\\sf y=\dfrac{1-\sqrt{3}}{2}\end{array}}$