Question

Find the value of $\sin {50}^{\circ }$.

Answer 1

Find the value of given trigonometric ratio :

Given trigonometric ratio: $\sin {50}^{\circ }$

$\sin {50}^{\circ }$can be expressed as, $\sin {50}^{\circ }=\sin ({30}^{\circ }+{20}^{\circ })$

We know that $$\sin (A+B)=\sin A\cos B+\cos A\sin B$$

So by applying the above formula we get,

$\sin {50}^{\circ }=\sin {30}^{\circ }\cos {20}^{\circ }+\cos {30}^{\circ }\sin {20}^{\circ }$

As, $\sin {30}^{\circ }=\frac{1}{2},\cos {20}^{\circ }=0.94,\cos {30}^{\circ }=\frac{\sqrt{3}}{2}$ and $\sin {20}^{\circ }=0.34$.

By substituting the values we get,

$$\begin{gathered} \sin {50}^{\circ }=\left(\frac{1}{2}\times 0.94\right)+\left(\frac{\sqrt{3}}{2}\times 0.34\right) \\ =0.47+\left(\frac{1.732}{2}\times 0.29\right)\mathbf{}[\because \sqrt{3}=1.732] \\ =0.47+0.29 \\ =0.76 \end{gathered}$$

Hence, the value of $\sin {50}^{\circ }$is $0.76$.