Question

prove theta = l/r ?​

Answer 1

That equation defines what radian measure is. Think about how you would write the same relation for degrees. You would use a proportion:

$\frac{l}{2\pi \: r} = \frac{ \alpha }{360}$

Rearranging a bit, we get the same relation as before, except with a scaling constant:

$l = \frac{2\pi}{360} r \alpha$

The trick is that we define radians in order to get rid of that scaling factor. To do that, we let 2Π radians correspond to 360 degrees. Then the proportion becomes

$\frac{l}{2\pi {r}^{2} } = \frac{ \alpha }{2\pi}$

And multiplying through by 2πr

$l = r \alpha$

hope it helps

Answer 2

Step-by-step explanation:

Prove that theta=(l)/(r), where theta is the angle in radian subt. Let in a circle,radius r,centre O, an arc AB of length l subtends an angle θ radian at centre. Show that : (1) l=rθ (2) Area of sector OAB=12r2θ What are the corresponding formula if ∠AOB=θ degree?

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