How to Find X and Y Coordinates on a Flipped Circle Using Javascript Methods
I Am Trying to Find the X, Y Points on a Circle Where 0 Degrees Starts at the Top of the Circle and Moves Clockwise. Typically, to Find the X, Y Coordinates on...
I am trying to find the X, Y points on a circle where 0 degrees starts at the top of the circle and moves clockwise. Typically, to find the x, y coordinates on a circle with a known radius and angle you could simply use the formula x = r(cos(degrees°)), y = r(sin(degrees°)). The circle would look like this and the degrees would expand counterclockwise from 0°.
However, I am using a circle where the 0° starts at the top and the degrees expand as one moves clockwise around the circle. Supposing that var r = 60; and var degrees = 130; what formula could I use (or javascript methods) to determine the X, Y values. Note: I can assume an origin point of 0, 60 because r = 60. Thanks.
3 Answers
As full circle has 2 radiants so you could calculate point coordinates for your circle with following formula:
x = radius * Math.sin(Math.PI * 2 * angle / 360);
y = radius * Math.cos(Math.PI * 2 * angle / 360);
var radius = 60;
var angle = 140;
var x = radius * Math.sin(Math.PI * 2 * angle / 360);
var y = radius * Math.cos(Math.PI * 2 * angle / 360);
console.log('Points coors are x='+
Math.round(x * 100) / 100 +', y=' +
Math.round(y * 100) / 100)The trick is to convert your problem into the problem you know how to solve. You can do this by subtracting 90 degrees from your angle and negating y, i.e. x=r cos(theta-90) and y = -r sin(theta-90). In JavaScript:
function circleXY(r, theta) {
// Convert angle to radians
theta = (theta-90) *
return {x: r*Math.cos(theta),
y: -r*Math.sin(theta)}
}
for (var theta=0; theta<=360; theta += 30) {
var answer = circleXY(60, theta);
console.log('(x, y) = ' + '(' + answer.x + ', ' + answer.y + ') for theta=' + theta);
}produces the following result:
(x, y) = (3.67394039744206e-15, 60) for theta=0
(x, y) = (30.000000000000007, 51.96152422706631) for theta=30
(x, y) = (51.96152422706632, 29.999999999999996) for theta=60
(x, y) = (60, 0) for theta=90
(x, y) = (51.96152422706632, -29.999999999999996) for theta=120
(x, y) = (30.000000000000007, -51.96152422706631) for theta=150
(x, y) = (3.67394039744206e-15, -60) for theta=180
(x, y) = (-29.999999999999986, -51.96152422706632) for theta=210
(x, y) = (-51.96152422706632, -29.999999999999996) for theta=240
(x, y) = (-60, -7.34788079488412e-15) for theta=270
(x, y) = (-51.96152422706631, 30.000000000000007) for theta=300
(x, y) = (-30.00000000000003, 51.961524227066306) for theta=330
(x, y) = (-1.1021821192326178e-14, 60) for theta=360
Should be
x = Math.cos(Math.PI * 2 * angle/360); and y = Math.sin(Math.PI * 2 * angle/360);
David Miller brings 15 years of experience in global economics, personal finance strategy, and market dynamics. He specializes in turning complex economic trends into actionable insights for everyday readers.
