Rapid Recall
- Which problems are you ready to present?
- Which problems did you sincerely attempt
- A force of 7 Newtons acts in a direction that is 60 degrees below the positive $x$-axis. Give the $x$ and $y$ components of the force.
- Give a polar equation of the curve $y=x^2$. (Substitute $x=r\cos\theta$ and $y=r\sin\theta$, and solve for $r$.)
- We know $x=r\cos\theta$. For the curve $r=2\sin\theta$, find $\frac{dx}{d\theta}$.
Group problems
- Consider the ray from the origin through the point $P=(-2,2)$. What's the angle between this ray and the positive $x$ axis? What the distance from the origin to $P$?
- Plot the polar points with $(r,\theta)$ given by $(3,0)$, $(4,\pi/3)$, $(-5,\pi/6)$, $(3,\pi/2)$, $(-3,\pi/2)$, $(-3,-\pi/2)$.
- Give a polar equation of the curve $2x+3y=4$. (So substitute $x=r\cos\theta$ and $y=r\sin\theta$, and then solve for $r$.)
- Give a Cartesian equation of the polar curve $r=\tan\theta\sec\theta$. (Use $x=r\cos\theta$ and $y=r\sin\theta$ to work backwards.)
- We know $x=r\cos\theta$ and $y=r\sin\theta$. Compute $dx$ in terms of $r, \theta,dr, d\theta$. (If you need to, assume that everything depends on $t$, compute derivatives, then multiply by $dt$.)
- Plot the curve $r=3-2\sin\theta$ in the $r\theta$ plane, and then in the $xy$ plane.
- Plot the curve $r=\sin\theta$ in the $r\theta$ plane, and then in the $xy$ plane.
- Plot the curve $r=2\sin3\theta$ in the $r\theta$ plane, and then in the $xy$ plane.
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