Find all numbers t such that (3/5,t) is a point on the unit circle.

Give exact answers in fraction form. Write your answers in ascending order.
t=?
t=?

Hello,

Point (⅗; t) is defined by:
{ x = ⅗
{ y = t

Since this point is on the unit circle, it fits the equation of that circle:
x² + y² = 1
(⅗)² + t² = 1
t² = 1 - (⅗)² = 1 - 9/25 = 25/25 - 9/25 = 16/25 = (⅘)²
t² - (⅘)² = 0
(t - ⅘)(t + ⅘) = 0
t = ±⅘

Thus the exact solution in fraction form and ascending order:
t = -⅘
t = +⅘

Regards,
Dragon.Jade :-)

We have x = 3/5.
Since the point is on the unit circle, we have r = 1.
Thus, we have:

x^2 + y^2 = r^2
(3/5)^2 + y^2 = 1^2
9/25 + y^2 = 1
y^2 = 16/25
y = ±4/5

Thus, since y= t, we have:
t = -4/5
t = 4/5