An ant starts on (0,3) on a circle with 3 radius and walks 2 units counterclockwise along the arc of a circle. Find the x and y coordinates of where the ant ends up.I only know how to move in a straight line (up-down, left-right) to determine coordinates.How would I begin to attempt this problem? I imagine I have to plug in a 2 into some sort of formula.

Question

An ant starts on (0,3) on a circle with 3 radius and walks 2 units counterclockwise along the arc of a circle. Find the   x and   y coordinates of where the ant ends up.I only know how to move in a straight line (up-down, left-right) to determine coordinates.How would I begin to attempt this problem? I imagine I have to plug in a 2 into some sort of formula.

Braylon Perez · Accepted Answer

o units counter-clockwise means that you&#039;re arclength traveled is 2. The formula for arclength is   S  =  θ  r. So, you have   2  =  θ  ∗  3. This gives you the subtended angle. Now, use trig to find   x and   y coordinates.      x    r    =  cos  ⁡  (  θ  )      y    r    =  sin  ⁡  (  θ  )

Brenden Tran · Accepted Answer

You probably know the equation for the circumference of a circle, that is   2  π  r. So for this circle, you know he circumference is   6  π units long. Now your ant only walked 2 units. So by ratio he walked       1          3      π       of the circle.Now you can plug these values into the we&#039;ll know formulae for angles and x,y coordinates and you&#039;ll find your answer. It won&#039;t be a nice exact point though.

An ant starts on (0,3) on a circle with 3 radius and walks 2 units counterclockwise along the arc of

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