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Question Number 34980 by NECx last updated on 14/May/18

$$Ifcos45°=\frac{1}{\sqrt{2}}.Findcos45.1°$$

Answered by ajfour last updated on 14/May/18

$$\cos (\frac{\pi }{4}+\frac{\pi }{1800})\approx \cos \left(\frac{\pi }{4}\right)-\frac{\pi }{1800}\sin \frac{\pi }{4}$$$$=\frac{1}{\sqrt{2}}(1-\frac{\pi }{1800})=0.707(1-\frac{0.0314}{18})$$$$=0.707(1-0.00173)$$$$\approx 0.707-0.0012\approx 0.7058.$$

Answered by tanmay.chaudhury50@gmail.com last updated on 14/May/18

$$y=cosx$$$$y+△y=cos(x+△x)herex={45}^{o}x+△x=45.1^o$$$$△y=cos(x+△x)-cosx$$$$\frac{△y}{△x}=\frac{dy}{dx}$$$$△y=\frac{dy}{dx}.△x$$$$△y=-sinx\times \frac{\mathrm{\Pi }}{1800}$$$$△y=-\left(\frac{1}{\sqrt{2}}\right)\times \frac{\mathrm{\Pi }}{1800}$$$$socos(45.1^o)=\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{2}}\times \frac{\mathrm{\Pi }}{1800}$$$$cos{(45.1)}^o=\frac{1}{\sqrt{2}}(1-\frac{\mathrm{\Pi }}{1800})$$$$cos{(45.1)}^o=\frac{\sqrt{2}}{2}\times (1-0.0017453293)$$$$cos{(45.1)}^o=0.7071067812\times 0.9982546707$$$$cos{(45.1)}^o=0.705872647$$$${180}^o=\mathrm{\Pi }radian$$$$1^o=\frac{\mathrm{\Pi }}{180}so{(0.1)}^o=\frac{\mathrm{\Pi }}{1800}$$$$$$

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