Answer:
[tex]\begin{gathered} \sin \theta=\frac{4\sqrt[]{15}}{23} \\ \cos \theta=\frac{17}{23} \end{gathered}[/tex]Explanation:
In a unit circle, the radius = 1 unit
The terminal side of angle θ intersects the unit circle in the first quadrant at x= 17/23.
From the equation of a unit circle, we have:
[tex]x^2+y^2=1^2[/tex]Substitute the given value of x:
[tex]\begin{gathered} (\frac{17}{23})^2+y^2=1^2 \\ y^2=1-(\frac{17}{23})^2 \\ y^2=\frac{240}{529} \\ y=\pm\sqrt[]{\frac{240}{529}} \\ y=\pm\frac{4\sqrt[]{15}}{23} \end{gathered}[/tex]Since angle θ is in the first quadrant, we take the positive value of y:
Therefore:
[tex]\begin{gathered} \sin \theta=\frac{y}{r} \\ \sin \theta=\frac{\frac{4\sqrt[]{15}}{23}}{1} \\ \sin \theta=\frac{4\sqrt[]{15}}{23} \end{gathered}[/tex]Similarly:
[tex]\begin{gathered} \cos \theta=\frac{x}{r} \\ \cos \theta=\frac{\frac{17}{23}}{1} \\ \cos \theta=\frac{17}{23} \end{gathered}[/tex]