Describe the sequence of transformations by which the graph \(y = \left| 2 \cos \left( x - \frac{\pi

Question

Describe the sequence of transformations by which the graph $y = \left| 2 \cos \left( x - \frac{\pi}{2} \right) \right|$ may be obtained from the graph of $y = \cos x$. Hence, sketch the graph of $y = \left| 2 \cos \left( x - \frac{\pi}{2} \right) \right|$, for $-\pi \leq x \leq \pi$. The graph of $y = |kx|$, where $k$ is a constant, passes through the maximum point of the curve of $y = \left| 2 \cos \left( x - \frac{\pi}{2} \right) \right|$ for $-\pi \leq x \leq \pi$. Find the possible value(s) of $k$ in terms of $\pi$.

Accepted Answer

(i) Translate $\pi/2$ units in the positive $x$-direction; stretch vertically by factor $2$; reflect the portions below the $x$-axis in that axis. The graph is $y=2|\sin x|$. (ii) $k=\pm4/\pi$.

Trigonometry - Trigonometric Graphs and Parameters

Trigonometry - Trigonometric Graphs and Parameters