Question

A particle moves along the polar curve r=4-2 costheta so that at time t seconds, theta=t^2.

Answer 1

Find the time t in the interval
1≤t≤2
for which the x-coordinate of the particle's position is -1.

Answer 2

This is what I have so far: x: 4cos(theta)-2cos^2(theta)+1=0 Do I have to find the roots?

Answer 3

Yes, but also recall that theta = t^2

Factor the quadratic and solve for theta, once you have that, you can then let t^2 = your solution and solve for t.

Answer 4

Oh, thanks so much. I had to work on other problems, because this one was confusing. My calculator can't do this. How accurate should my roots be?

Answer 5

I was thinking of just using the quadratic formula, is that possible considering I have trig functions?

Answer 6

Correct, you can use the quadratic formula, just remember that your roots will have to be equal to cos(theta) instead of x, then solve for theta, then t.

Answer 7

Thanks again. You're the best.

Answer 8

Not a problem, glad I could help, about to head to bed soon, but best of luck on reaching the solution.