Question

Calcule através das regras de operações com arco :
A) sen 15º
B) TG 75º
C) cos 105º
D) sen 135º

Answer 1

a) $sen 15 = sen (45+30)=sen45.cos30+sen30.cos45=\frac{\sqrt{2} }{2} .\frac{\sqrt{3} }{2} +\frac{1}{2} .\frac{\sqrt{2} }{2} =\frac{\sqrt{6} }{4}  +\frac{\sqrt{2} }{4} =\frac{\sqrt{6} +\sqrt{2} }{4}$

b)

c) $cos 105=cos(60+45)=cos60.cos45-sen60.sen45=\frac{1}{2}.\frac{\sqrt{2} }{2}-\frac{\sqrt{3} }{2} .\frac{\sqrt{2} }{2}   =\frac{{\sqrt{2} } }{4} -\frac{\sqrt{6} }{4} =\frac{\sqrt{2}-\sqrt{6}  }{4}$

d) $sen 135=sen(90+45)=sen90.cos45+sen45.cos90=1.\frac{\sqrt{2} }{2} +\frac{\sqrt{2} }{2} .0=\frac{\sqrt{2} }{2}+0=\frac{\sqrt{2} }{2}$