Dilations
Recall:
𝑦=𝑎𝑓𝑥 vertically dilates by a factor of 𝑎
𝑦=𝑓𝑏𝑥 horizontally dilates by a factor of 1𝑏
For 𝑓𝑥=𝑎sin𝑏𝑥 and 𝑔𝑥=𝑎cos𝑏𝑥, (with 𝑎≠0 and 𝑏≠0)
Amplitude=𝑎 and Period=2𝜋𝑏 
So, to find 𝑎 and 𝑏 you can always choose
𝑎=Amplitude and 𝑏=2𝜋Period