Question

prove that cos60°=1/2

Answer 1

Draw a Right Angled Triangle with One angle 60 Degrees. Thus this becomes a 30–60–90 Degrees Triangle. Let’s call it a Triangle ABC. Let angle A be 60 Degrees, let angle B be 90 Degrees, so naturally angle C is 30 Degrees.

For a 30–60–90 Degrees Triangle, side opposite to angle 30 Degrees is half the hypotenuse. So in our case if side AB is x then side AC is 2x and side BC is

sqrt(3)*x.

In a Right Angled Triangle, Cos of certain angle is defined as Adjacent Side divided by Hypotenuse.

Therefore Cos(60) would be AB/AC, which is x/2x, which is 1/2.

Thus it is proved that Cos(60) is 1/2.