Question

Given this unit circle what is the value of y

Answer 1

Given,

The expression is,

$\cos x=\frac{5}{8}$

The trigonometric ratio is,

$\begin{gathered} \cos x=\frac{\text{base}}{\text{hypotenuse}} \\ \text{Here, On comparing,} \\ \text{Base = 5} \\ \text{Hypotenuse = 8} \end{gathered}$

By pythagorus theorem,

$\begin{gathered} Hypotenuse^2=perpendicular^2+base^2 \\ 8^2=P^2+5^2 \\ 64-25=P^2| \\ P=\sqrt[]{39} \end{gathered}$

For the y coordinates of the point on the unit circle,

$\begin{gathered} \sin x\text{ =}\frac{perpendicular}{hypotenuse} \\ \sin x\text{ =}\frac{\sqrt[]{39}}{8} \end{gathered}$

Hence, the y coordinate is sqrt(39)/8.