Prove that S is equal to r theta
Or
Theta equals s over r
Or
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. Clearly, arc LM subtends ∠LOM at the centre O. Now, take an arc LN of length equal to the radius of the circle and join 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 LNθ = 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
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