Question

Evaluate the exact value of the following expression.sine and cosecant of 60°

Answer 1

To evaluate:

$\sin 60^{\circ}\text{ and }co\sec 60^{\circ}$

As we know,

Using the trigonometric ratio for sine,

$\begin{gathered} \sin \theta=\frac{Opp}{\text{Hyp}} \\ \sin 60^{\circ}=\frac{\sqrt[]{3}}{2} \end{gathered}$

Using the trigonometric ratio for cosecant,

$\begin{gathered} co\sec \theta=\frac{\text{Hyp}}{\text{Opp}} \\ co\sec 60^{\circ}=\frac{2}{\sqrt[]{3}} \end{gathered}$

Hence, the answers are,

$\begin{gathered} \sin 60^{\circ}=\frac{\sqrt[]{3}}{2} \\ \cos ec60^{\circ}=\frac{2}{\sqrt[]{3}} \end{gathered}$