Prove that S is equal to r theta
Theta equals s over r
s r theta formula
Prove that the radian measure of any angle at the centre of a circle is equal to the ratio of the arc subtending that angle at the centre to the radius of the circle.Let, XOY be a given angle. Now, with centre O and any radius OL draw a circle. Suppose the drawn circle intersects OX and OY at L and M respectively. ON.
Then, by definition, ∠LON = 1 radian.
Since the ratio of two arcs in a circle is equal to the ratio of the angles subtended by the arcs at the center of the circle, hence,∠LOM/∠LON = arc LM/arc LN
θ = s/r, [i.e. theta equals s over r]
or, s = r θ, [i.e. s r theta formula]
Therefore, now we know the meaning of “S is equal to r theta”
● Measurement of Angles