Question

$\sin 35°$ in fraction from.

Answer 1

consider $\sin 35°$

$$\begin{gathered} \sin 35°=\sin \left(30°+5°\right) \\ =\sin 30°\cos 5°+\sin 5°\cos ° \\ but\sin 30°=\frac{1}{2},\cos 30°=\frac{\sqrt{3}}{2} \\ but5°=5\times \frac{\mathrm{\pi }}{180} \\ =5\times \frac{22}{7\times 180} \\ =\frac{5}{60} \\ =\frac{1}{12} \\ \therefore sin5°=\frac{1}{12} \\ \cos 5°=\sqrt{1-{\sin }^{2}5°} \\ =\sqrt{1-{\left(\frac{1}{12}\right)}^2} \\ =\sqrt{1-\frac{1}{144}} \\ =\sqrt{\frac{144-1}{144}} \\ =\sqrt{\frac{143}{144}} \\ ∾1 \end{gathered}$$

Now, consider $$\begin{gathered} \sin \left(30°+5°\right)=\sin 30°\cos 5°+\cos 30°\sin 5° \\ =\frac{1}{2}\times 1+\frac{\sqrt{3}}{2}\times \frac{1}{12} \end{gathered}$$

On simplify we have

$$\begin{gathered} \sin 35°=0.5+0.07 \\ =0.57 \\ =\frac{57}{100} \end{gathered}$$

Hence, $\sin 35°$ in fraction form is $\frac{57}{100}$