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Mathematics
Mathematics
Problem
Consider the equation
2
sin
x
+
3
=
0
2\sin x+\sqrt{3}=0
2
sin
x
+
3
=
0
. (i) Solve
sin
x
=
−
3
2
\sin x=-\dfrac{\sqrt{3}}{2}
sin
x
=
−
2
3
for
0
∘
≤
x
≤
360
∘
0^{\circ}\le x\le360^{\circ}
0
∘
≤
x
≤
36
0
∘
. (ii) Using your result from part (i), find all the solutions of
2
sin
x
+
3
=
0
2\sin x+\sqrt{3}=0
2
sin
x
+
3
=
0
in the interval
0
∘
≤
x
≤
720
∘
0^{\circ}\le x\le720^{\circ}
0
∘
≤
x
≤
72
0
∘
. (iii) State the total number of distinct solutions obtained in part (ii).
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