How do I calculate point P on a circle when I have the following information:

Radius=7

Arc Length=3

Angle in degrees=0.42857

Angle in rounded degrees 25

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The fact that the arc length is 3 and he radius is 7 is a complete specification of the size of the angle

which is length of arc/length of circle =angle in radians /2π

angle in radians=2π×3/(2π×7)=3/7 radians = (180/π)×3/7 degrees=24.55533408

Either start at the x-axis and go up 3/7 radian or calculate the rectangular coordinates as

x=7cos(3/7) y=7sin(3/7) with radians set

x=7cos(24.55533408) y=7sin(24.55533408) with degrees set

I worked out 25^{0} is approximately 0.4 radians so I am going to solve that way.

Consider the line from the center (0,0) of the circle to the point like a vector.

X = r cos(θ) =

Y = r sin(θ) =

So put your calculator in radians mode

and plug the values into the equations using θ = 0.42857 rad.

Or put your calculator in degrees mode

and plug the values into the equations using θ = 25 degrees.

and plug the values into the equations using θ = 25 degrees.

There are other ways and equations to use to get the answer, but those are to me

the easiest to learn; and they will be useful when you take physics too.

Important note: Those equations always work, but Only when you use the angle to the + x axis. So if you are given a different angle use your geometry of a circle 360^{0}, a line 180^{0}, and a right angle 90^{0} to find the angle to the + x axis - then proceed.

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