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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
- 9 years agoFavorite 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