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Manipal Entrance Test 2013 Math Paper
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© examsnet.com
Question : 54
Total: 80
If
x
,
y
∈
[
0
,
2
π
]
then the total number of ordered pairs
(
x
,
y
)
satisfying
sin
x
.
cos
y
=
1
is equal to
1
3
5
7
Validate
Solution:
sin
x
cdot
cos
y
=
1
⇒
sin
x
=
1
,
cos
y
=
1
or
sin
x
=
−
1
,
cos
y
=
−
1
if
sin
x
=
1
,
cos
y
=
1
⇒
x
=
π
2
,
y
=
0
,
2
π
if
sin
x
=
−
1
,
cos
y
=
−
1
⇒
x
=
3
π
2
,
y
=
π
Thus possible ordered pairs are
(
π
2
,
0
)
,
(
π
2
,
2
π
)
,
(
3
π
2
,
π
)
© examsnet.com
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