Random number generation - code not working as it should - matlab

Question

So I have to generate a random number (called 'p' here) between 0 and 90 whose frequency distribution is a cosine function (i.e I should have more numbers between 0 and 45 than numbers between 45 and 90).
I am working on matlab
The code is as follows -
flag = 1;
while flag == 1
candidate = randi([0,90]);
if rand < cosd( candidate )
p = candidate;
flag = 2;
end
end
I am generating 20 such numbers but always I get most of the numbers towards the higher end (45-90).
From those 20 numbers, there is hardly 1-2 numbers < 45.
Is my code wrong?
EDIT: Okay, so I got the answer. I tried running the code separately as follows-
for i = 1:20
flag = 1;
while flag == 1
candidate = randi([0,90]);
if rand < cosd( candidate )
p = candidate;
flag = 2;
disp(p);
end
end
end
And I'm getting most of the values of p between 0 and 45. My original code had an external 'if' condition which was the reason for only accepting higher values of 'p'. I used a while loop and the number of iterations were much more than 20 to get 20 values of 'p'.
Here is my original code snippet -
while zz <=20
d = randi([0,359]);
flag = 1;
while flag == 1
c = randi([0,90]);
x = rand(1);
if x < cosd(c)
p = c;
flag = 2;
end
end
if 'external condition'
strike(zz) = d;
dip(zz) = p;
slip(zz) = round(i);
zz= zz+1;
end
end

Answer 1

If you just want to get answer, read the last line. But if you want to know that why that answer is right, read the explanation.
Assume that you have a distinct distribution function like this:
f(0)=1;
f(1.5)=10;
f(4)=9;
So the cumulative function is:
F(0)=1;
F(1.5)=11;
F(4)=20;
No we want to have a relative cumulative function, as F(4)=20 (4 is the last item), we divide cumulative function by 20. So it would be:
F'(0)=0.05
F'(1.5)=0.55
F'(4)=1.00
Now, we generate a random number between 0 and 1. Every time we generate a random number, we generate a value for F'(x) and if F'(x) does not have that value anywhere, we use nearest bigger number (like y) which for some x, F(x)=y. For my example, based on relative cumulative function:
If the random number was less than 0.05, our distribution-based random number is 1.5
If the random number was between 0.05 and 0.55, our distribution-based random number is 2,
If was more than 0.55, our distribution-based random number is 4
We should do a similar work with continuous distribution functions. The difference is that in continuous world, we use integral instead of cumulative function. So for your question, we have:
f(x)=cos(x) , 0<=x<=90
F(x)=sin(x)-sin(0)=sin(x) , 0<=x<=90
F'(x)=cos(x) , 0<=x<=90 (Because F(90)=1)
Now we generate a random number between 0 and 1 (like r). So we have:
F'(x)=r => sin(x)=r => x=arcsin(r)
Actually, you just need to generate a random number between 0 and 1 and calculate the arcsin of that.