The terminal side of counterclockwise angle theta passes through (x, y) with length r. The horizontal distance from the origin to (x, y) is x, and the vertical distance is y. A dashed segment from (x, y) meets the x-axis at a right angle.
sin θ = yrcsc θ = rycos θ = xrsec θ = rxtan θ = yxcot θ = xy (4.1)
A right triangle with legs ay and b meeting at a right angle, and hypotenuse c opposite the right angle.

Pythagorean theorem

c2 = a2 + b2(4.2)
A right triangle with vertex Ay between the horizontal leg and hypotenuse. The horizontal leg is the side adjacent to Ay, and the vertical leg is the side opposite Ay.
sin A = side opposite Ahypotenusecsc A = hypotenuseside opposite Acos A = side adjacent Ahypotenusesec A = hypotenuseside adjacent Atan A = side opposite Aside adjacent Acot A = side adjacent Aside opposite A(4.5)

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