Find the period,sub interval,build table and sketch graph

Question

Given 𝑦 = 1 - sin(2𝑥 - 𝜋) , 0 ≤ 𝑥 ≤ 2𝜋

a) Find the period.

b) Find the subinterval.

c) Build table of values for 𝑦 and 𝑥.

d) Sketch the graph for 0 ≤ 𝑥 ≤ 2𝜋

Answer 1

Since this is a negative sine graph we know it will start at 0 then go to its minimum, back to zero , and then to its max and then back to 0

Period = 2pi/b it this equation b=2 so period = 2pi/b=pi if period is pi then your graphing point are pi/4 apart

To find the phase shift set the inside of the function = 0 so 2x-pi=0 x=pi/2

vertical shift or midline is +1

I cant sketch it but I have given you all the info you need to do it