Question

Point A is the terminal point on the unit circle associated with real number pi/5. What are the coordinates of this point?

Answer 1

In polar coordinates, we represent the points as:

P = (R, θ)

Where R is the radius and θ is the angle (depending on how you want to work, you can use θ in degrees or radians).

Then in this case we know that we are working with the unit circle, whose radius is R = 1.

And the angle is pi/5.

Then our point will be:

P = (1, pi/5).

Now we also could write it in rectangular coordinates, knowing that for a point (R, θ) we have:

x = R*cos(θ)

Y = R*sin(θ)

Then for our point the rectangular coordinates are:

x = 1*cos(pi/5) = 0.81

y = 1*sin(pi/5) = 0.59

Then the point is (0.81, 0.59)