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Mathematics
Mathematics
Problem
Find all values of
θ
\theta
θ
in
0
≤
θ
<
2
π
0\le\theta<2\pi
0
≤
θ
<
2
π
satisfying
sin
2
θ
=
cos
θ
\sin2\theta=\cos\theta
sin
2
θ
=
cos
θ
. a)
θ
=
π
6
,
7
π
6
,
5
π
6
,
11
π
6
\theta=\dfrac{\pi}{6},\dfrac{7\pi}{6},\dfrac{5\pi}{6},\dfrac{11\pi}{6}
θ
=
6
π
,
6
7
π
,
6
5
π
,
6
11
π
b)
θ
=
π
2
,
3
π
2
\theta=\dfrac{\pi}{2},\dfrac{3\pi}{2}
θ
=
2
π
,
2
3
π
c)
θ
=
π
6
,
π
2
,
5
π
6
,
3
π
2
\theta=\dfrac{\pi}{6},\dfrac{\pi}{2},\dfrac{5\pi}{6},\dfrac{3\pi}{2}
θ
=
6
π
,
2
π
,
6
5
π
,
2
3
π
d)
θ
=
π
6
,
5
π
6
\theta=\dfrac{\pi}{6},\dfrac{5\pi}{6}
θ
=
6
π
,
6
5
π
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