Question

Resolva em R
a) sin 2x= V3/2
b) sin x= -1/2
c) cos x = -V3/2
d) tg x = -1

Answer 1

a)
sin(2x)= v.3/2
sin(2x)= 3/2v
2sin(2x)/3= v
v= 2sin(2x)/3

b) sin(x) = -1/2
sin(x) = -1/2
sin(π-x)= -1/2
x= arcsin(-1/2)
π-x= arcsin(-1/2)
x= -π/6
π-x= -π/6
x= -π/6 + 2kπ
π-x= -π/6 + 2kπ
x= 11π/6 + 2kπ
x= 7π/6 - 2kπ

x= 11π/6 + 2kπ
     7π/6 + 2kπ

c) cos(x) = -v.3/2
cos(x) = -3/2v
2cos(x)/3 = -v
-v = 2cos(x)/3
v = -2cos(x)/3

d) tan(x) = - 1
tan(x) = - 1,x <> π/2 + kπ
x = arctan (-1)
x = -π/4
x = -π/4 + kπ
x = 3π/4 + kπ
x <> π/2 + kπ
x= 3π/4 + kπ