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Question Number 198604 by ajfour last updated on 22/Oct/23

Commented by ajfour last updated on 22/Oct/23

$$\theta +\varphi =\alpha \left(known\right)$$$$radiusofarcisunity.$$$$Ifthetwoshadedpartsareequal,$$$$find\theta =f\left(\alpha \right).$$

Answered by mr W last updated on 22/Oct/23

$$\frac{\alpha R^2}{2}=\frac{R\cos \theta \times \left(R\cos \theta \right)\tan \alpha }{2}$$$${\cos }^2\theta =\frac{\alpha }{\tan \alpha }$$$$\Rightarrow \theta ={\cos }^{-1}\sqrt{\frac{\alpha }{\tan \alpha }}$$$$example:\alpha =45°,\Rightarrow \theta \approx 27.6°$$

Commented by ajfour last updated on 22/Oct/23

$$Thankyou!sir.$$$$\alpha =\frac{\pi }{4}\Rightarrow \cos {}^2\theta =\frac{\pi }{4}as\tan \frac{\pi }{4}=1$$

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