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## Conversion between radians and degrees

π radians = 180˚

## Finding arc length (using formula Arc length = (Ө/360˚)2πr)

**Arc length = (Ө/360˚**

**)2πr , Ө is given in degrees.**

## Finding arc length (using formula Arc length S = rӨ)

**Arc length S = rӨ , Ө must be in radians.**

<This formula is also given in the formula sheet for N and O level exams. I just memorise it anyway since it is so easy to remember.>

Take note not to confuse when to use the two formulae for finding arc length. It all depends on whether the angle subtended by the arc is given in degrees or radians. One common mistake is that students just stick to using one formula and assume the formula works for all questions disregarding whether the given angle is in degrees or radians.

<This formula is also given in the formula sheet for N and O level exams. I just memorise it anyway since it is so easy to remember.>

Take note not to confuse when to use the two formulae for finding arc length. It all depends on whether the angle subtended by the arc is given in degrees or radians. One common mistake is that students just stick to using one formula and assume the formula works for all questions disregarding whether the given angle is in degrees or radians.

## Finding area of sector of circle (using formula Area = (Ө/360˚)πr²)

**Area of sector of circle = (Ө/360˚)πr² , Ө is in degrees.**

## Finding area of sector of circle (using formula Area = (1/2)r²Ө)

**Area of sector of circle = (1/2)r²Ө , Ө must be in radians.**

<This formula is also given in the formula sheet for N and O level exams. I remember this formula as it is quite easy to remember. The A grade student can already remember all the necessary formulae in the O level formula sheet though it is given anyway during exam to refer to. Why is it that A grade students can remember formulae so well? There is no miracles here. Such students have practised so thoroughly well that even if they want to forget the formulae, it is almost impossible to forget since they have used the formulae so many times before.>

The following video shows how this formula is derived from the usual formula of Area of sector = (Ө/360˚) X πr². Just replace 360˚ in the formula by 2π radians (note that this is exactly converting degrees to radians). Then, simplify the formula and the formula for area of sector when angle Ө is in radians will then be derived as Area = (1/2) X r²Ө.

Try it for yourself to see! Doing it yourself beats seeing and hearing alone! Experience comes from doing and making mistakes, and learning from mistakes, and keep on repeating the same process of doing and learning from mistakes over and over again until perfection is achieved!

<This formula is also given in the formula sheet for N and O level exams. I remember this formula as it is quite easy to remember. The A grade student can already remember all the necessary formulae in the O level formula sheet though it is given anyway during exam to refer to. Why is it that A grade students can remember formulae so well? There is no miracles here. Such students have practised so thoroughly well that even if they want to forget the formulae, it is almost impossible to forget since they have used the formulae so many times before.>

The following video shows how this formula is derived from the usual formula of Area of sector = (Ө/360˚) X πr². Just replace 360˚ in the formula by 2π radians (note that this is exactly converting degrees to radians). Then, simplify the formula and the formula for area of sector when angle Ө is in radians will then be derived as Area = (1/2) X r²Ө.

Try it for yourself to see! Doing it yourself beats seeing and hearing alone! Experience comes from doing and making mistakes, and learning from mistakes, and keep on repeating the same process of doing and learning from mistakes over and over again until perfection is achieved!

## Solving question on finding segments of circles

In this following video, the formulae for

**area of sector =****(1/2)r²Ө**and**area of triangle = (1/2)absinӨ****(in this question both a and b are the radii of the circle so the area of triangle can also be seen as (1/2)r²sinӨ)**are used. Note that all angles are calculated in radians in this question. Make sure the calculator is set in radians mode too when doing calculations!