(2 sin θ - 1) (sin θ -2) = C Find θ
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Use trig identity
cos
2
a
=
cos
2
a
−
sin
2
a
=
1
−
2
sin
2
a, to transform the equation -->
−
(
1
−
2
sin
2
t
)
−
sin
t
=
0
2
sin
2
t
−
sin
t
−
1
=
0
.
Solve this quadratic equation for sin t
Since a + b + c = 0, use shortcut. the 2 real roots are:
sin
t
=
1
and
sin
t
=
c
a
=
−
1
2
.
Trig Table and unit circle -->
a.
sin
t
=
1
->
t
=
π
2
.
b.
sin
t
=
−
1
2
-> 2 solution arcs -->
t
=
−
(
π
6
)
and
t
=
7
π
6
Since the arc
11
π
6
is co-terminal to arc
(
−
π
6
)
, therefor, the answers for
(
0
,
2
π
)
are:
π
2
,
7
π
6
,
and
11
π
6
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