1. Convert the following from polar coordinates (r,θ) to Cartesian coordinates (x,y) with r>0 and 0 ≤ θ ≤ 2π radians.
   1. (7.0711, $\frac{\mathrm{\pi }}{4}$) = (__________ , __________)
   2. (536, $\frac{5\mathrm{\pi }}{6}$) = (__________ , __________)
2. Convert the following the given Cartesian coordinates (x,y) to polar coordinates (r,θ) with r>0 and 0 ≤ θ ≤ 2π radians.
   1. (40,41) = (__________ , __________)
   2. (275,252) = (__________ , __________)
3. Rewrite x² + y² = 7y as a polar equation.
4. Rewrite r = 4 sin θ as a Cartesian equation.
5. Set Desmos to polar grid with the mode in radians. The following shape is the result of using the polar variables r, θ, and the sine function. Write the function that generated the following graph:
   
6. For the parametric equations:
   x(t)= a sin(bt)
   y(t)= c sin(dt)
   
   Find the values of a, b, c, and d for the following graph in the parametric form (a cos(bt),c sin(dt)).
   1. = ____
   2. = ____
   3. = ____
   4. = ____
7. A ball is thrown at 609 cm/s perpendicular to the direction of RipStik traveling at 346 cm/s as seen in the diagram. The velocity vector for the ball over the ground is given by the sum of the velocity of the RipStik plus the launch velocity for the ball: v_ground = v_ripstik + v_ball
   
   1. __________ Calculate the magnitude (length) for the velocity vector of the ball over the ground.
   2. __________ Calculate the direction angle θ for the velocity vector of the ball in degrees.
8. __________ A tractor tire is pulled with a force F of 900 Newtons at an angle of 20° for a distance d of 10 meters. Use the dot product Fd_distancecos(θ) to calculate the work done (energy expended). Round answer to nearest whole number.
   
9. __________ A tractor tire is pulled with a force of 900 Newtons at an angle of 20°. The tire pivots about a point that is 1.5 meters behind the attachment point. Use 1.5 meters as the lever arm. Use the cross product Fd_{lever arm}sin(θ) to calculate the torque exerted on the tire.