| Exam Board | SPS |
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| Module | SPS FM Pure (SPS FM Pure) |
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| Year | 2024 |
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| Session | June |
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| Topic | Implicit equations and differentiation |
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12. A curve \(C\) is given by the equation
$$\sin x + \cos y = 0.5 \quad - \frac { \pi } { 2 } \leqslant x < \frac { 3 \pi } { 2 } , - \pi < y < \pi$$
A point \(P\) lies on \(C\).
The tangent to \(C\) at the point \(P\) is parallel to the \(x\)-axis.
Find the exact coordinates of all possible points \(P\), justifying your answer.
(Solutions based entirely on graphical or numerical methods are not acceptable.)
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