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Given this unit circle what is the value of y

Given this unit circle what is the value of y-example-1
User Alberto Rivelli
by
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1 Answer

20 votes
20 votes

Given,

The expression is,


\cos x=(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{ =}(perpendicular)/(hypotenuse) \\ \sin x\text{ =}\frac{\sqrt[]{39}}{8} \end{gathered}

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

User Ltk
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