91Ó°ÊÓ

Since the equation of a unit circle is given by \(x^2 + y^2 = 1\), we can plug in the coordinates of the given point to get the following equation: \[t^2 + \left(-\frac{2}{5}\right)^2 = 1\]

Now we need to solve the equation for t. First, simplify the equation by squaring \(-\frac{2}{5}\): \[t^2 + \frac{4}{25} = 1\] Now, isolate t squared by subtracting \(\frac{4}{25}\) from both sides of the equation: \[t^2 = 1 - \frac{4}{25}\] Next, convert 1 to a fraction with a denominator of 25: \[t^2 = \frac{25}{25} - \frac{4}{25}\] Subtract the fractions: \[t^2 = \frac{21}{25}\] Finally, take the square root of both sides of the equation to find t. Remember that there are two possible solutions for t, one is positive and the other is negative. \[ t = \pm \sqrt{\frac{21}{25}}\] So, the two possible values for t are: \[t = \pm \frac{\sqrt{21}}{5}\] Thus, there are two points on the unit circle with a y-coordinate of \(-\frac{2}{5}\): \(\left(\frac{\sqrt{21}}{5}, -\frac{2}{5} \right)\) and \(\left(-\frac{\sqrt{21}}{5}, -\frac{2}{5}\right)\).