Help please huhu as much as possible computerized solution so that i can read and undertand clearly, thank you so much

THEOREM 8.2.1 Tests for Symm- Thc graph of a polar equation is symmetric with respect to: (i) they-Ind! if replacing (r. 9) by (r. 1r -- 9) results in anequivalenlequallon (ii) the x-nxis if replacing (r. 0) by (r. -9) results in an equivalent equation (iii) the origin if replacing (r. 0) by { -r, 0) results in an equivalent equation 4. a.) Use (ii) and (iii) of Theorem 8.2.1 to show that graph of the polar equation 1'2 = 1 + c056 is symmetric with respect to x-axis and to the origin. b.) As a consequence of the two symmetries demonstrated in part (a), the graph must also be symmetric with respect to the y-axis. Show, however, that (i) of Theorem 8.2.1 fails to prove this symmetry. c.) Find an alternative test that proves yaxis symmetry. d.) Use a graphing utility to obtain the graph of the equation. [Hint: Use the functions 1' = 1/1 + c050 and r = \\l1 + cos.]