Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Find all values of
θ
∈
[
0
,
2
π
)
\theta\in[0,2\pi)
θ
∈
[
0
,
2
π
)
that satisfy
cos
2
θ
=
1
2
\cos 2\theta=\dfrac12
cos
2
θ
=
2
1
. a)
{
π
3
,
2
π
3
,
4
π
3
,
5
π
3
}
\Big\{\dfrac{\pi}{3},\,\dfrac{2\pi}{3},\,\dfrac{4\pi}{3},\,\dfrac{5\pi}{3}\Big\}
{
3
π
,
3
2
π
,
3
4
π
,
3
5
π
}
b)
{
π
6
,
5
π
6
,
7
π
6
,
11
π
6
}
\Big\{\dfrac{\pi}{6},\,\dfrac{5\pi}{6},\,\dfrac{7\pi}{6},\,\dfrac{11\pi}{6}\Big\}
{
6
π
,
6
5
π
,
6
7
π
,
6
11
π
}
c)
{
π
6
,
2
π
3
,
7
π
6
,
5
π
3
}
\Big\{\dfrac{\pi}{6},\,\dfrac{2\pi}{3},\,\dfrac{7\pi}{6},\,\dfrac{5\pi}{3}\Big\}
{
6
π
,
3
2
π
,
6
7
π
,
3
5
π
}
d)
{
π
3
,
5
π
3
}
\Big\{\dfrac{\pi}{3},\,\dfrac{5\pi}{3}\Big\}
{
3
π
,
3
5
π
}
Browse the problem library