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Question
Mathematics
If sin θ = (24/25) and 0° < θ < 90° then what is the value of sin ( (θ/2) ) ?
Q. If
sin
θ
=
25
24
and
0
∘
<
θ
<
9
0
∘
then what is the value of
sin
(
2
θ
)
?
7781
226
Trigonometric Functions
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A
25
12
26%
B
25
7
26%
C
5
3
33%
D
5
4
15%
Solution:
We have,
sin
θ
=
25
24
,
0
∘
<
θ
<
9
0
∘
cos
2
θ
=
1
−
sin
2
θ
=
1
−
(
25
24
)
2
Since lies in first quadrant
⇒
cos
θ
=
25
7
cos
θ
=
1
−
2
sin
2
2
θ
2
sin
2
2
θ
=
1
−
cos
θ
=
1
−
25
7
2
sin
2
2
θ
=
25
18
sin
2
2
θ
=
25
9
⇒
sin
2
θ
=
±
5
3
⇒
sin
2
θ
=
5
3
[Negative sign discarded since
θ
is in first quadrant]