Answer:
5
Step-by-step explanation:
sin
u
=
5
13
. First, find cos u.
cos
2
u
=
1
−
sin
2
u
=
1
−
25
169
=
144
169
-->
cos
u
=
±
12
13
.
Since u is in Quadrant 2, then, cos u < 0.
cos
u
=
−
12
13
.
To find
cos
(
u
2
)
, apply trig identity:
2
cos
2
(
u
2
)
=
1
+
cos
u
=
1
−
12
13
=
1
13
cos
2
(
u
2
)
=
1
26
-->
cos
(
u
2
)
=
±
1
√
26
.
Sin u is in Quadrant 2, then
u
2
is in Quadrant 1, and
cos
(
u
2
)
is positive:
cos
(
u
2
)
=
1
√
26
=
√
26
26
To find
sin
(
u
2
)
, apply the trig identity:
sin
u
=
2
sin
(
u
2
)
.
cos
(
u
2
)
sin
(
u
2
)
=
sin
u
2
cos
(
u
2
)
=
(
5
13
)
(
√
26
2
)
=
5
√
26
26
tan
(
u
2
)
=
sin
(
u
2
)
cos
(
u
2
)
=
(
5
√
26
26
)
(
√
26
)
=
5
