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. **

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 LNor, ∠LOM/1 radian = arc LM/radius OL

or, ∠LOM = arc LM/radius OL × 1 radian = arc LM/ radius OL radian.

Therefore, circular measures of ∠LOM is arc LM/radius OL

If θ be the circular measure of ∠LOM, arc LM = s and radius of the circle = OL = r then,

** θ = s/r**, [i.e.

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**

**Sign of Angles****Trigonometric Angles****Measure of Angles in Trigonometry****Systems of Measuring Angles****Important Properties on Circle****S is Equal to R Theta****Sexagesimal, Centesimal and Circular Systems****Convert the Systems of Measuring Angles****Convert Circular Measure****Convert into Radian****Problems Based on Systems of Measuring Angles****Length of an Arc****Problems based on S R Theta Formula**

**From S is Equal to R Theta to HOME PAGE**

**Didn't find what you were looking for? Or want to know more information
about Math Only Math.
Use this Google Search to find what you need.**

## New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.