Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

---
Lv 6
--- asked in Education & ReferenceHomework Help · 9 years ago

Please help me (rates of change )!!!!!!!!!!!!!!!!!!!!!!!!!!!!!?

As a particle moves around a circle , its angular velocity is given by dtheta/dt = 1/1+t^2

show that pi/4 < theta < 3pi/4 (or equal to) and explain why the particle never moves through an angle of more than pi/2

1 Answer

Relevance
  • 9 years ago
    Favorite Answer

    To solve for theta, you need to integrate...

    d_theta/d_t = 1/(1+t^2)

    Recall from your identities that the integral of 1/(1+t^2) is arctan(t)

    theta = arctan(t)

    Now also recall from your trig identities that tan(pi/4) = 1 and tan(3*pi/4) = -1, after which it just resets...well, it's easier to see if you draw the graph of y = tan(x)

    Finally, the particle can't go through an angle of pi/2 because tan(pi/2) = asymptote

Still have questions? Get your answers by asking now.