The shit blog of Paul Chris Jones

What are 'cosine' and 'sine'?

Let's say you draw a diagonal line. You know how long the line is, and what angle it's at to the x-axis.

(1) But how far have you gone sideways (in the x direction)?

(2) And how far have you gone up (in the y direction)?

The answer to (1) is length x cos45 = 0.707

The answer to (2) is length x sin45 = 0.707 as well.

What's 'cos45'? You can put it into a calculator by pressing the 'cos' button and typing 45 in brackets after it. Cos stands for 'cosine' and 'sin' is short for 'sine'.

Let's do another.

Here, the length of the line is still 1, but the angle (to the x-axis) is zero.

(1) What's the distance travelled sideways?

(2) What's the distance travelled up?

Answer to (1): 1 x cos0 = 1

Answer to (2): 1 x sin0 = 0

These answers make sense, because the line has gone sideways, not up at all.

One more, but this time, let's make the angle super-large.

Here, the angle is 315 degrees and the line length is still 1.

(1) What's the distance travelled on the x-axis?

(2) And for the y axis?

The answer to (1) is 1 x cos 315 = 0.707

The answer to (2) is 1 x sin 315 = - 0.707

In summary, the equations are:

length x cos (angle) = distance travelled in x-axis direction

length x sin (angle) = distance travelled in y-axis direction

Some questions I can't answer: Why does the line have to rotate anti-clockwise? Why does it have to start at the x-axis?