difficulty to use "sin" function

Consider following:

T = 0.02;                       %period (sec)
w = 2 * pi / T;                 %w = 314.1593, angqular frequency (rad/sec)
t = 0 : 0.01 : 20;              %time vector (sec)
x = sin(w*t);
plot(t,x)

What is wrong with MATLAB? A sine plot does not look like above. When I set w = 314.1593, the above figure will be plotted. Sine function is a periodic function. But above plot is something completely different. Maximum value should be equal to 1.0 but it is about 10e-12. I cannot figure out where is the problem?

[Stephen23]

You are plotting integer multiples of pi:

>> w*t(1:8)
ans =
    0.00000    3.14159    6.28319    9.42478   12.56637   15.70796   18.84956   21.99115

What is sine of any integer multiple of pi ?

Answer 1

[Mehmed Saad]

Either increase you sampling rate

T = 0.02;                       %period (sec)
w = 2 * pi / T;                 %w = 314.1593, angqular frequency (rad/sec)
t = 0 : 0.001 : 20;              %time vector (sec)
x = sin(w*t);
plot(t,x)

or add a phase in sin

T = 0.02;                       %period (sec)
w = 2 * pi / T;                 %w = 314.1593, angqular frequency (rad/sec)
t = 0 : 0.01 : 20;              %time vector (sec)
x = sin(w*t+pi/10);
plot(t,x)

Answer 2

[Walter Roberson]

Your w is approximately 100*pi and your t values are all integer multiples of 1/100 . When you multiply the two together, you get an integer multiple of 1/100 * 100*pi which will give you an integer multiple of pi. sin() of an integer multiple of pi is 0 to within round-off error. SO what you are plotting is just round-off error.