Moderate -0.8 This is a straightforward C3 question testing basic understanding of cosec and modulus. Part (a) requires simple conversion to sin x = 1/2 and finding standard angles. Part (b) tests graph recognition and reflection in x-axis. Part (c) extends (a) trivially by including negative values. All steps are routine with no problem-solving required.
Solve the equation \(\operatorname { cosec } x = 2\), giving all values of \(x\) in the interval \(0 ^ { \circ } < x < 360 ^ { \circ }\).
(2 marks)
The diagram shows the graph of \(y = \operatorname { cosec } x\) for \(0 ^ { \circ } < x < 360 ^ { \circ }\).
\includegraphics[max width=\textwidth, alt={}, center]{9fd9fa54-b0e6-413d-8645-de34b99b859a-03_609_1045_559_479}
The point \(A\) on the curve is where \(x = 90 ^ { \circ }\). State the \(y\)-coordinate of \(A\).
Sketch the graph of \(y = | \operatorname { cosec } x |\) for \(0 ^ { \circ } < x < 360 ^ { \circ }\).
Solve the equation \(| \operatorname { cosec } x | = 2\), giving all values of \(x\) in the interval \(0 ^ { \circ } < x < 360 ^ { \circ }\).
(2 marks)
3
\begin{enumerate}[label=(\alph*)]
\item Solve the equation $\operatorname { cosec } x = 2$, giving all values of $x$ in the interval $0 ^ { \circ } < x < 360 ^ { \circ }$.\\
(2 marks)
\item The diagram shows the graph of $y = \operatorname { cosec } x$ for $0 ^ { \circ } < x < 360 ^ { \circ }$.\\
\includegraphics[max width=\textwidth, alt={}, center]{9fd9fa54-b0e6-413d-8645-de34b99b859a-03_609_1045_559_479}
\begin{enumerate}[label=(\roman*)]
\item The point $A$ on the curve is where $x = 90 ^ { \circ }$. State the $y$-coordinate of $A$.
\item Sketch the graph of $y = | \operatorname { cosec } x |$ for $0 ^ { \circ } < x < 360 ^ { \circ }$.
\end{enumerate}\item Solve the equation $| \operatorname { cosec } x | = 2$, giving all values of $x$ in the interval $0 ^ { \circ } < x < 360 ^ { \circ }$.\\
(2 marks)
\end{enumerate}
\hfill \mbox{\textit{AQA C3 2007 Q3 [7]}}