Find the exact coordinates of the points on a circle of radius 12.5 at an angle of 180°
180º is the negative x direction
x = -12.5 , y = 0
(12.5,0)
Well, if we're talking about a circle of radius 12.5, we're basically talking about a giant pizza. And if the pizza has an angle of 180°, it means someone took a huge bite out of it. So, the exact coordinates of the points on this half-eaten pizza would be a little tricky to determine. But hey, at least we can enjoy the remaining half of the pizza!
To find the coordinates of points on a circle of radius 12.5 at an angle of 180°, we can use the unit circle definition.
The unit circle has a radius of 1 unit, and the points on the circle can be represented as (cosθ, sinθ), where θ is the angle.
To find the coordinates on a circle with a radius of 12.5, we need to scale the coordinates by the radius.
Given an angle of 180° and a radius of 12.5, we can calculate the coordinates as follows:
cos(180°) = -1
sin(180°) = 0
So, the coordinates of the point on the circle at an angle of 180° with a radius of 12.5 are (-12.5, 0).
To find the exact coordinates of points on a circle with a given radius at a specific angle, you can use the trigonometric functions sine and cosine.
For a circle with radius 12.5, the x-coordinate of a point on the circle at an angle of 180° is given by:
x = r * cos(angle)
And the y-coordinate is given by:
y = r * sin(angle)
Substituting the values, we have:
x = 12.5 * cos(180°)
y = 12.5 * sin(180°)
Now we can calculate the coordinates.
Using a scientific calculator or a math library that supports trigonometric functions, we have:
x = 12.5 * cos(π) = 12.5 * (-1) = -12.5
Similarly,
y = 12.5 * sin(π) = 12.5 * 0 = 0
Therefore, the coordinates of the point on the circle with a radius of 12.5 at an angle of 180° are (-12.5, 0).