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Mathematics
Mathematics
Problem
The set of all possible values of
θ
\theta
θ
in the interval
(
0
,
π
)
(0, \pi)
(
0
,
π
)
for which the points
(
1
,
2
)
(1, 2)
(
1
,
2
)
and
(
sin
θ
,
cos
θ
)
(\sin \theta, \cos \theta)
(
sin
θ
,
cos
θ
)
lie on the same side of the line
x
+
y
=
1
x + y = 1
x
+
y
=
1
is (a)
(
0
,
π
2
)
\left(0, \frac{\pi}{2}\right)
(
0
,
2
π
)
(b)
(
π
4
,
3
π
4
)
\left(\frac{\pi}{4}, \frac{3\pi}{4}\right)
(
4
π
,
4
3
π
)
(c)
(
0
,
3
π
4
)
\left(0, \frac{3\pi}{4}\right)
(
0
,
4
3
π
)
(d)
(
0
,
π
4
)
\left(0, \frac{\pi}{4}\right)
(
0
,
4
π
)
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