Standard +0.8 This requires solving a trigonometric equation involving both sin x and cos² x, necessitating the identity cos² x = 1 - sin² x to convert to a quadratic in sin x, then solving the quadratic and finding multiple solutions in a given range. This goes beyond routine trigonometric equation solving and requires multi-step algebraic manipulation and careful consideration of the domain.
The diagram shows a sketch of part of the curve with equation \(y = 2\sin x + 3\cos^2 x - 3\). The curve crosses the \(x\)-axis at the points O, A, B and C.
\includegraphics{figure_15}
Find the value of \(x\) at each of the points A, B and C. [7]
The diagram shows a sketch of part of the curve with equation $y = 2\sin x + 3\cos^2 x - 3$. The curve crosses the $x$-axis at the points O, A, B and C.
\includegraphics{figure_15}
Find the value of $x$ at each of the points A, B and C. [7]
\hfill \mbox{\textit{WJEC Unit 1 2024 Q15 [7]}}