/sci/ - Science & Math

TURBO brainlet here, but how the FUCK do I find the five key points of a trigonometric graph?

I understand using default values like 0, pi/2, pi, 2pi/3 and then 2pi but for stuff like

y=sin(2x) where the period changes obviously to just pi since period = 2pi/B

pic related are the values that were worked in the book for the above equation

how did they get them? I can understand what do kind of I just need to know what they did mathematically to get those points!!!