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Question Number 57700 by Nameed last updated on 10/Apr/19

$$\mathrm{R}(1-\cos \theta )=0.5$$$$\mathrm{Rsin}\theta =4$$$$\mathrm{R}=?$$$$\theta =?$$

Answered by tanmay.chaudhury50@gmail.com last updated on 10/Apr/19

$$R\times 2sin\frac{\theta }{2}cos\frac{\theta }{2}=4$$$$R\left(2{sin}^2\frac{\theta }{2}\right)=\frac{1}{2}$$$$\frac{2{Rsin}^2\frac{\theta }{2}}{2Rsin\frac{\theta }{2}cos\frac{\theta }{2}}=\frac{1}{2\times 4}$$$$tan\frac{\theta }{2}=\frac{1}{8}\to \theta =2{tan}^{-1}\left(\frac{1}{8}\right)$$$$sin\frac{\theta }{2}=\frac{1}{\sqrt{8^2+1^2}}=\frac{1}{\sqrt{65}}$$$$R\times 2{sin}^2\frac{\theta }{2}=\frac{1}{2}$$$$R\times 2\times \frac{1}{65}=\frac{1}{2}$$$$R=\frac{65}{4}$$

Commented by math1967 last updated on 10/Apr/19

$$tan\frac{\theta }{2}=\frac{1}{8}\therefore \theta ={2\tan }^{-1}\frac{1}{8}$$

Commented by tanmay.chaudhury50@gmail.com last updated on 10/Apr/19

$$thankyoudada...votearkikhabar...kolkatate$$

Commented by math1967 last updated on 11/Apr/19

$$Jorprocharcholche$$

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