Describe the sequence of transformations by which the graph $y = \cos x$ may be obtained from the

Question

Describe the sequence of transformations by which the graph $y = \cos x$ may be obtained from the graph of $y = \left| 2 \cos \left( x - \frac{\pi}{2} \right) \right|$. 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) A: Translation of $\frac{\pi }{2}$ units in the positive $x$-direction. B: Scaling by a factor of $2$ parallel to the $y$ axis. C: Reflect the negative $y$ portion to positive about the x axis. Omit the negative $y$ portion (where $y<0$). (ii) $k=\pm \frac{4}{\pi }$

Trigonometric Functions and Graphs

Trigonometric Functions and Graphs