Drawing lines at increasing angles - drawing

Question

I'm not very good at math or geometry, but I want to draw some line segments at increasing angles. What I want to draw is something like when you hold your hand up and spread your fingers apart: lines that start at a common point and expand out at angles that have an equal difference between them.
I have tried this:
len = 300;
angle = 10;
for (i = 0; i <= 5; ++i) {
endPointX = 50 + len * Math.cos(angle);
endPointY = 50 + len * Math.tan(angle);
draw.Line(50, 50, endPointX, endPointY);
angle += 10;
}
However, that's totally wrong and produces something like this
http://i.stack.imgur.com/taX40.png
But I want something like this (bad mspaint, sorry):
http://i.stack.imgur.com/8xfpp.png
What's the right math for this?

Answer 1

There are two separate issues in your question, I will cover each.
Here's an ASCII picture of your situation:
B
+
/|
/ |
/ |
/ |
len / | y
/ |
/ |
/ |
/ __|
/ θ | |
+----------+
A x C
This is a right triangle. It has three sides:
The diagonal side in the picture opposite to the 90° angle is called the hypotenuse and has a length len. The hypotenuse is what you're trying to draw.
The vertical side is the side opposite to the angle θ and has a length y.
The horizontal side is the side adjacent to the angle θ and has a length x.
Given the above illustration the following equations are true:
cos(θ) = x/len
sin(θ) = y/len
These equations are another way of saying:
The cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse.
The sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse.
When solving the equation for x and y, you get:
x = len * cos(θ)
y = len * sin(θ)
So you want sin() and cos(), not cos() and tan(). If the point A is not at the origin, you would need to offset x and y by addition, like so:
x = len * cos(θ) + 50
y = len * sin(θ) + 50
With the values for x and y, you can find the coordinates for point B on the triangle, and thus be able to draw your lines.
Also, assuming you're programming in Java, the trigonometric functions in the Math class expect the angle in radians, not degrees. Lots of programming languages that provides trigonometric functions are like this.
Radians and degrees measure the same thing, but a complete rotation in degrees goes from 0 to 360° while a complete rotation in radians go from 0 to 2π.
To convert angles in degrees to radians, multiply the angle by π/180. In Java, the constant π is provided by Math.PI.
For example, an angle of 10° degrees is equivalent to 10 * π/180, or π/18 radians.

Answer 2

Firstly, you want cos and sin, not cos and tan.
Secondly, most maths libraries perform trigonometric functions in radians, not degrees. So 10 is a very large difference indeed! To convert from degrees to radians, multiply by (pi/180).

Answer 3

You shouldn't be using tan, but sin. If I remember correctly, it should be something like:
Math.cos(angle/180);
-Math.sin(angle/180);
The negative on sin is important.

Answer 4

The reason you are getting uneven looking angles is that every time you add 10 you're actually spinning the line around the circle 1.6 times.
The math functions expect angles to be in radians, not degrees.
360 degrees = 2*Math.PI radians.
Instead of 10, write "2*Math.PI/36.0"
Also, use sin instead of tan.