You can do a table for several values of tha angle (Ф).
But first you should remember some properties of the sine function.
1) Range: sine function goes from - 1 to + 1.
That means that 2 sin (πФ) goes from - 2 to + 2.
2) sine(0) = 0 => 2sin(π0) = 0
3) sine (π/2) = 1 =>
Ф = 0.5 => sin(π*0.5) = sin(π/2) = 1
=> 2sin(π*0.5) = 2
3) sin (-π/2) = - 1 =>
Ф = -0.5 => 2sin(-π/2) = -2
4) Periodicity:
The period of sine function is 2π
=> sin (πФ+ 2π) = sin(πФ)
Now you can do the table
Ф πФ sin(πФ) 2sin(πФ)
-1 -π sin(-π) 2sin(-π) = 0
-5/6 -5π/6 sin(-5π/6) 2sin(-5π/6) = -1
-1/2 -π/2 sin(-π/2) 2sin(-π/2) = -2
-1/6 -π/6 sin(-π/6) 2sin(-π/6) = -1
0 0 sin(0) 2sin(0) = 0
1/6 π/6 sin(π/6) 2sin(π/6) = 1
1/2 π/2 sin(π/2) 2sin(π/2) = 2
5/6 5π/6 sin(5π/6) 2sin(5π/6) = 1
1 π sin(π) 2sin(π) = 0
Then you can see that one cycle is from Ф = -1/2 to Ф = 1/2
And so you know that you can draw the function in that interval [-1/2, 1/2] and you already have some conspicuos values (from -2 to +2).
You can add some other points to do a better sketch.
