Given a point on the circle at (4/15, y).
In a unit circle, the endpoint (x, y) is equal to (cos θ, sin θ).
Since x = cos θ and x = 4/15, then cos θ = 4/15.
Now, we know that cos θ = adjacent/hypotenuse, therefore, adjacent (x) = 4 and hypotenuse (r) = 15.
Let's solve for the opposite side (y) using the Pythagorean Theorem.
[tex]\begin{gathered} r^2=x^2+y^2 \\ 15^2=4^2+y^2 \\ 225=16+y^2 \\ 225-16=y^2 \\ 209=y^2 \\ \sqrt[]{209}=\sqrt[]{y^2} \\ \sqrt[]{209}=y \end{gathered}[/tex]The value of the opposite side is √209.
Now, we know that sin θ = opposite over hypotenuse therefore, sin θ =√209/15
[tex]\sin \theta=\frac{\sqrt[]{209}}{15}[/tex]To summarize, here are the values of cos θ and sin θ.
[tex]\begin{gathered} \cos \theta=\frac{4}{15} \\ \sin \theta=\frac{\sqrt[]{209}}{15} \end{gathered}[/tex]
