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Nov 2015 p13 q7
575
The diagram shows part of the graph of \(y = a \, \cos x - b\), where \(a\) and \(b\) are constants. The graph crosses the \(x\)-axis at the point \(C(\cos^{-1} c, 0)\) and the \(y\)-axis at the point \(D(0, d)\). Find \(c\) and \(d\) in terms of \(a\) and \(b\).
Solution
To find \(c\), we use the fact that the graph crosses the \(x\)-axis at \(C(\cos^{-1} c, 0)\). At this point, \(y = 0\), so:
\(a \, \cos(\cos^{-1} c) - b = 0\)
\(a \, c - b = 0\)
\(c = \frac{b}{a}\)
To find \(d\), we use the fact that the graph crosses the \(y\)-axis at \(D(0, d)\). At this point, \(x = 0\), so: