*If possible can everything be done on paper and sent from photos**I also attached the Textbook*
1. When a projectile is fired with an initial velocity of 𝑣0 ft/s at an angle 𝛼 above the horizontal at sea levelwith zero air resistance, then its (distance, height) at time 𝑡 can be derived from Newton’s laws, and are
given by (𝑥,𝑦)=(𝑣0𝑡cos𝛼,−𝑔2𝑡2 +𝑣0𝑡sin𝛼), where 𝑔=32 ft/s2.
A hunting rifle is fired with a muzzle velocity of 3000 ft/s at an angle 𝛼. Pick four values of 𝛼 between 1° and
89°, and for each find how far the bullet will travel before hitting the ground, and the maximum height of
the bullet. Use a graphing device to sketch the four paths of the bullet on the 𝑥,𝑦-plane.
2.a. Choose a polar curve 𝑟 =𝑓(𝜃) that’s interesting to you. 𝑓 must involve sine or cosine. State the equation
𝑟 =𝑓(𝜃) that you choose. Sketch the graph of 𝑟=𝑓(𝜃) in 𝑟 vs. 𝜃 Cartesian coordinates. Then, use it to
sketch the polar curve 𝑟 =𝑓(𝜃) in the 𝑥,𝑦-plane. Explain how your graph is made by discussing its features
as is done in chapter 10.3 EXAMPLEs 7,8. Use complete sentences.
2.b. Find an equation of the tangent line to your polar curve at 𝜃 =𝜋/6. Include the tangent line in your
sketch in the 𝑥,𝑦-plane.
3.a. Use a graphing device to sketch the polar curve 𝑟=1+cos3𝜃 in the 𝑥,𝑦-plane. Shade the region
contained in one loop of the polar curve. What values of 𝜃 correspond to this region?
3.b. Find the area of the region you shaded. Show your work.