What does derive mean in the syllabus? 2U math trig functions (1 Viewer)

[Danneo]

The formula l = r(theta), for the length l of an arc subtending an angle at the centre of a circle of radius r, should be derived
I dont understand what derive means in this context. THX

Btw does any have 3U math in focus? THX again

 

[HeroWise]

ok so basically I think what its asking is

How do you find a perimeter of the sectors arc? (in degrees) theta/360 * 2pi*r
If we convert to radians: (we know 360 is 2pi)
theata/(2pi) * (2pi*r) the 2pi gets cancelled leaving with
theta * r = length of arc


Thats the possible derivation in the syllabus im not sure

 

[fan96]

Derive basically means you prove it.

The arc length formula can be proved using the definition of the radian.

1 radian is the angle subtended at the centre by an arc which is equal in length to the radius.

In other words, the angle (in radians) subtended at the centre is a ratio of the arc length to the radius.

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This also shows why the angle MUST be in radians for the formula to work.