3 Jia has to solve the equation
$$2 - 2 \sin ^ { 2 } \theta = \cos \theta$$
where \(- 180 ^ { \circ } \leq \theta \leq 180 ^ { \circ }\)
Jia's working is as follows:
$$\begin{gathered}
2 - 2 \left( 1 - \cos ^ { 2 } \theta \right) = \cos \theta
2 - 2 + 2 \cos ^ { 2 } \theta = \cos \theta
2 \cos ^ { 2 } \theta = \cos \theta
2 \cos \theta = 1
\cos \theta = 0.5
\theta = 60 ^ { \circ }
\end{gathered}$$
Jia's teacher tells her that her solution is incomplete.
3
- Explain the two errors that Jia has made.
3 - Write down all the values of \(\theta\) that satisfy the equation
$$2 - 2 \sin ^ { 2 } \theta = \cos \theta$$
where \(- 180 ^ { \circ } \leq \theta \leq 180 ^ { \circ }\)