what is trigonometry?Watch
If the angle formed between Ox and OP is theta, therefore P(cos(theta), sin(theta)).
Mr - wait not Mr but Sir - so Sir Trigonometry finds its roots in the unit circle. It is the circle of centre (0,0) and radius r=1. A point P on the circle is defined as the cosine (which would be the x-axis) and the sine (the y-axis) of the angle formed between the x-axis and the line OP in a new unit: the radian. We have one full turn of the unit circle being 2pi radians (as perimeter is 2pi r and r is here 1). Each angle of Ox with OP is therefore a fraction of 2pi. More specifically, 90 degrees=pi/2 radians etc...
Broadly speaking it connects distances along circles to distances along straight lines. That is trigonometry. 'Sine' and 'cosine' are just the names we give to the functions that connect these two types of distance.
Someone will correct me if I'm wrong, but I believe trigonometry was invented to find the distance to stars moving in the sky in a circular motion. So if you are looking at a star at some angle x, then the height of that star perpendicular to the ground is called sinx and the distance from where you're looking to the perpendicular is called cosx. We can then define the rest of trigonometry from these values.
As I've said we're defining functions - sine and cosine - that connect distances along circles - the circle centred at you and radius from you to the star - to distances along straight lines - the ones you described.