Chapter 6.1, Problem 61E

Finding the Terminal Point for $\frac{\pi }{6}$. Suppose the terminal point determined by $t=\frac{\pi }{6}$ is $P\left(x,y\right)$ and the points Q and R are as shown in the figure. Why are the distances PQ and PR the same? Use this fact, together with the Distance Formula, to show that the coordinates of P satisfy the equation $2y=\sqrt{x^2+{\left(y-1\right)}^2}$. Simplify this equation using the fact that $x^2+y^2=1$. Solve the simplified equation to find $P\left(x,y\right)$.