The cos(α) function is a trigonometric functions whose values are between -1 and 1. So for all α in [0°; 360°]: -1 ≤ cos(α) ≤ 1 is always true.

The cos function can be seen in the unit circe:

The value of cos(135°) is the length of the green side of the triangle, in this particular case -0,707.

In a right triangle the equation cos(α) = adjacent leg / hypotenuse always holds. In case of the unit circle the length of the hypotenuse of the triangle is always 1. So cos(α) = adjacent leg.

Some important angles:

cos(0°) = 1

cos(90°) = 0

cos(135°) = -0,707

cos(180°) = -1

cos(270°) = 0

cos(360°) = 1

The cos(α) function can also be displayed in a coordinate system, shown in the picture below.

Where can you use the cos function?

Imagine, you want to stitch the first letter of your name. In my example, let it be an A.

We need a needle and an embroidery frame.

Step 0: Make a drawing, like the following one.

Step 1: Turn left 70 degrees.

Step 2: Move 200 steps.

Step 3: Turn right 140 degrees. (Turn right 70° to get to the direction of the beginning, another 70° to turn down on the right side of the A.)

Step 4: Move 140 steps.

Step 5: Turn right 110 degrees. (Because of symmetry we know the blue angle is also 70°. So the red one must be 110° because 180° - 70° = 110°.)

Step 6: Move 280 * cos(70) steps. (We see a little right triangle in the middle. cos(70°) = x / 140, so x = cos(70°) * 140. x is the half length of y, so y = 280 * cos(70°).

Step 7: Turn right 180 degrees.

Step 8: Move 280 * cos(70) steps. (We have to move back).

Step 9: Turn right 70 degrees.

Step 10: Move 200 - 140 steps. (We have to move the last 60 steps).

Code: