The point p is on the unit circle find p(x,y) from the given information
The y coordinate of p is -3/5 and the x coordinate is positive
P(x,y) =
P(x,y) = (x, -3/5)
Since the y-coordinate is -3/5, we know that y = -3/5.
And since the x-coordinate is positive, we know that x > 0.
To find the coordinates of point P on the unit circle, we can use the following formula:
x = cos(θ)
y = sin(θ)
Given that the y-coordinate of point P is -3/5 and the x-coordinate is positive, we can determine the values of x and y as follows:
x = cos(θ)
y = sin(θ) = -3/5
Since the x-coordinate is positive, we know that 0° < θ < 180°, which corresponds to the first and second quadrants on the unit circle.
Using the Pythagorean identity sin^2(θ) + cos^2(θ) = 1, we can determine the value of cos(θ) as follows:
(-3/5)^2 + cos^2(θ) = 1
9/25 + cos^2(θ) = 1
cos^2(θ) = 1 - 9/25
cos^2(θ) = 16/25
cos(θ) = ± √(16/25)
cos(θ) = ± 4/5
Since the x-coordinate is positive, we can conclude that cos(θ) = 4/5.
Therefore, the coordinates of point P can be written as P(x, y) = (4/5, -3/5).
To find the point P(x, y) on the unit circle, we can use the given information.
The unit circle is a circle with a radius of 1 centered at the origin (0,0) in a 2D coordinate system. This means that the distance from the origin to any point on the unit circle is 1.
Given that the y-coordinate of point P is -3/5 and the x-coordinate is positive, we can determine the x-coordinate using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the hypotenuse is the radius of the unit circle, which is 1. The y-coordinate (-3/5) is the length of one side, and we are looking for the length of the other side, which is the x-coordinate.
Let's denote the x-coordinate as a variable, say x. By applying the Pythagorean theorem, we have:
x^2 + (-3/5)^2 = 1^2
Simplifying the equation:
x^2 + 9/25 = 1
Subtracting 9/25 from both sides:
x^2 = 16/25
Taking the square root of both sides:
x = ±√(16/25)
Since the given information states that the x-coordinate is positive, we can ignore the negative square root. Thus, we have:
x = √(16/25)
Simplifying the square root:
x = 4/5
Therefore, the point P(x, y) on the unit circle is:
P(4/5, -3/5)