Answer:
θ
can be in the first quadrant
0
≤
θ
≤
90
or the fourth quadrant
270
≤
θ
≤
360
If
θ
is in the first quadrant,
then
sin
θ
=
5
13
cos
θ
=
12
13
tan
θ
=
5
12
Therefore,
sin
2
θ
=
2
sin
θ
cos
θ
=
2
×
5
13
×
12
13
=
120
169
cos
2
θ
=
cos
2
θ
−
sin
2
θ
=
(
12
13
)
2
−
(
5
13
)
2
=
144
169
−
25
169
=
119
169
If
θ
is in the fourth quadrant,
then
sin
θ
=
−
5
13
cos
θ
=
12
13
tan
θ
=
−
5
12
Therefore,
sin
2
θ
=
2
sin
θ
cos
θ
=
2
×
−
5
13
×
12
13
=
−
120
169
cos
2
θ
=
cos
2
θ
−
sin
2
θ
=
(
12
13
)
2
−
(
−
5
13
)
2
=
144
169
−
25
169
=
119
169
