point P on a circle

Question

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

Answer 1

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

 

Answer 2

I worked out 25⁰ 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.

 

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 360⁰, a line 180⁰, and a right angle 90⁰ to find the angle to the + x axis - then proceed.