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Question Number 12132 by tawa last updated on 14/Apr/17

$$\mathrm{Given}\mathrm{that}1°=0.017\mathrm{rad}$$$$\mathrm{Use}\mathrm{f}\left(\mathrm{a}\right)=\sin \left(\mathrm{a}\right)\mathrm{to}\mathrm{find}\mathrm{an}\mathrm{approximate}\mathrm{value}\mathrm{for}\sin \left(29\right)°.$$

Answered by mrW1 last updated on 14/Apr/17

$$\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}=\frac{f(x+\mathrm{\Delta }x)-f\left(x\right)}{\mathrm{\Delta }x}\approx \frac{dy}{dx}$$$$\Rightarrow f(x+\mathrm{\Delta }x)\approx f\left(x\right)+\frac{dy}{dx}\mathrm{\Delta }x$$$$y=f\left(x\right)=\sin x$$$$\frac{dy}{dx}=\cos x$$$$\sin 29°=\sin (30-1)\approx \sin 30°+\frac{dy}{dx}\times \mathrm{\Delta }x$$$$=\frac{1}{2}-\frac{\sqrt{3}}{2}\times 0.0175=0.4848$$

Commented by tawa last updated on 14/Apr/17

$$\mathrm{wow},\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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