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Mathematics
Mathematics
Problem
Solve
cos
2
θ
=
sin
θ
\cos 2\theta = \sin\theta
cos
2
θ
=
sin
θ
for
θ
∈
[
0
,
2
π
)
\theta\in[0,2\pi)
θ
∈
[
0
,
2
π
)
. a)
{
π
3
,
2
π
3
,
3
π
2
}
\Big\{\dfrac{\pi}{3},\,\dfrac{2\pi}{3},\,\dfrac{3\pi}{2}\Big\}
{
3
π
,
3
2
π
,
2
3
π
}
b)
{
π
6
,
5
π
6
,
3
π
2
}
\Big\{\dfrac{\pi}{6},\,\dfrac{5\pi}{6},\,\dfrac{3\pi}{2}\Big\}
{
6
π
,
6
5
π
,
2
3
π
}
c)
{
π
6
,
5
π
6
}
\Big\{\dfrac{\pi}{6},\,\dfrac{5\pi}{6}\Big\}
{
6
π
,
6
5
π
}
d)
{
π
2
,
7
π
6
,
11
π
6
}
\Big\{\dfrac{\pi}{2},\,\dfrac{7\pi}{6},\,\dfrac{11\pi}{6}\Big\}
{
2
π
,
6
7
π
,
6
11
π
}
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