Cone created from Sector of Circle

Question

Suppose I use a sector of circle with radius 1 to create a cone (by joining the radius of the sector).

How do I express radius of cone in terms of $\theta$? Is it

$$\sin{\frac{\theta}{2}} = r, \qquad \cos{\frac{\theta}{2}} = h$$?

Answer 1

Note that slant height $s$ has value $1$ .

$$\sin \frac{\theta}{2} =\frac{r}{s} \Rightarrow r = \sin \frac{\theta}{2}$$