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

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

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

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

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

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