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

polivijuye

polivijuye

Answered question

2022-06-17

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.

Answer & Explanation

Braylon Perez

Braylon Perez

Beginner2022-06-18Added 34 answers

o units counter-clockwise means that you'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

Brenden Tran

Beginner2022-06-19Added 9 answers

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'll know formulae for angles and x,y coordinates and you'll find your answer. It won't be a nice exact point though.

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