Additional Mathematics – Trigonometry | e-Consult

Answer 1

• Amplitude \(=|3| = 3\).
• Period \(= \dfrac{2\pi}{|2|}= \pi\).
• Phase shift: set \(2x-\frac{\pi}{4}=0\Rightarrow x=\frac{\pi}{8}\). The graph is shifted \(\frac{\pi}{8}\) units to the right.
• Mid‑line crossings occur when the argument of the sine is a multiple of \(\pi\):

  \[

  2x-\frac{\pi}{4}=k\pi\quad(k\in\mathbb Z)

  \]

  For \(k=0\): \(x=\frac{\pi}{8}\) → point \(\left(\frac{\pi}{8},\,0\right)\).
  

  For \(k=1\): \(2x-\frac{\pi}{4}=\pi\Rightarrow x=\frac{5\pi}{8}\) → point \(\left(\frac{5\pi}{8},\,0\right)\).