\( \def\dfrac#1#2{\displaystyle\frac{#1}{#2}} \def\solve#1{\begin{array}{rcl}#1\end{array} } \)

Home / 08 Trigonometric Functions / 04 Finding Points On Unit Circle

Example: Determine the coordinate(s) of a point if the point is known to be on the Unit Circle.

\[ P\left(x,\dfrac{\sqrt{{5}} }{{3}}\right) \]

Solution To find the missing coordinate, we use the equation \(x^2+y^2=1\) and solve. \[ \solve{ x^2+\left(\dfrac{\sqrt{ 5 } }{ 3 }\right)^2 &=& 1\\ x^2 &=&1 - \dfrac{{5}}{{9}}\\ x^2 &=& \dfrac{{4}}{{9}}\\ x&=&\pm\dfrac{{2}}{{3}} } \]

x^2+y^2=1;{color:black}\ (2/3,\frac{\sqrt{ 5 }}{ 3 });{color:black} \ (-2/3,\frac{\sqrt{ 5 } }{ 3 });{color:black}