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Mathematics
Mathematics
Problem
Solve the equation
sin
(
2
θ
−
π
)
=
sin
(
θ
+
π
3
)
\sin\bigl(2\theta-\pi\bigr)=\sin\bigl(\theta+\tfrac{\pi}{3}\bigr)
sin
(
2
θ
−
π
)
=
sin
(
θ
+
3
π
)
. a. (i) Derive the general solution for
θ
\theta
θ
. b. (ii) Hence find all values of
θ
\theta
θ
in the interval
0
≤
θ
<
2
π
0 \le \theta < 2\pi
0
≤
θ
<
2
π
that satisfy the equation.
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