Answer:
θ
=
41.3
∘
,
138.7
∘
,
221.3
∘
,
318.7
∘
Step-by-step explanation:
3
sin
2
θ
−
10
(
1
−
2
sin
2
θ
)
=
0
23
sin
2
θ
−
10
=
0
sin
2
θ
=
10
23
sin
θ
=
±
√
10
23
θ
=
arcsin
(
√
10
23
)
=
41.3
∘
θ
=
arcsin
(
−
√
10
23
)
=
−
41.3
∘
+
360
∘
=
318.7
∘
We missed the solutions in quadrants 2 and 3 as arcsin is restricted to quadrants 1 and 4:
So:
41.3
∘
+
180
∘
=
221.3
∘
318.7
∘
−
180
∘
=
138.7
∘
Step-by-step explanation:
There you go