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7. Solve the following trigonometric equations for 0 ✓ < 2⇡. (a) 2 sin2 ✓ � 3 = �3 cos ✓ (b) sin ⇣ 3✓ + ⇡ 18 ⌘ = 1 8. solve the triangle if a = 2, c = 1 and a = 120�. 9. given an = 12 ✓ �1 2 ◆n , write the first five terms of the sequence. 10. find the nth term an of a sequence whose first four terms are ⇢ � 8 11 , 9 22 ,�10 33 , 11 44 , . . . � 11. find the sum 15x k=1 (2k2 � 4k + 6) 12. find the number of terms of the finite arithmetic sequence {7, 16, 25, 34, . . . , 574}. 13. in an arithmetic sequence, the 12th term is 52 and the 51st term is 208. find the nth term formula and then find the 172nd term. 14. find the sum of the first 40 terms of the arithmetic sequence {1, 6, 11, 16, . . .}. 15. write the nth term formula for the geometric sequence {3, 6, 12, 24, . . .}. 16. find the sum of the first 30 terms of the sequence {�1, 2,�4, 8, . . .}. 17. find the sum of the infinite geometric series, if possible: (a) 1x n=1 4 ✓ 1 2 ◆n�1 (b) 2 + 8 + 32 + 128 + . . . 18. use the binomial theorem to expand (2x3 � y)4. 19. find an equation for the parabola with directrix at x = 3 and focus (�1,�1). find the two latus rectum points and graph the parabola labeling all important points. 20. find the center, major axis, vertices, and foci of the ellipse 3x2 +4y2 � 12x+8y+4 = 0. graph by hand and label. list answers as exact values, not decimal approximations. 2⇡.="" (a)="" 2="" sin2="" ✓="" �="" 3="�3" cos="" ✓="" (b)="" sin="" ⇣="" 3✓="" +="" ⇡="" 18="" ⌘="1" 8.="" solve="" the="" triangle="" if="" a="2," c="1" and="" a="120�." 9.="" given="" an="12" ✓="" �1="" 2="" ◆n="" ,="" write="" the="" first="" five="" terms="" of="" the="" sequence.="" 10.="" find="" the="" nth="" term="" an="" of="" a="" sequence="" whose="" first="" four="" terms="" are="" ⇢="" �="" 8="" 11="" ,="" 9="" 22="" ,�10="" 33="" ,="" 11="" 44="" ,="" .="" .="" .="" �="" 11.="" find="" the="" sum="" 15x="" k="1" (2k2="" �="" 4k="" +="" 6)="" 12.="" find="" the="" number="" of="" terms="" of="" the="" finite="" arithmetic="" sequence="" {7,="" 16,="" 25,="" 34,="" .="" .="" .="" ,="" 574}.="" 13.="" in="" an="" arithmetic="" sequence,="" the="" 12th="" term="" is="" 52="" and="" the="" 51st="" term="" is="" 208.="" find="" the="" nth="" term="" formula="" and="" then="" find="" the="" 172nd="" term.="" 14.="" find="" the="" sum="" of="" the="" first="" 40="" terms="" of="" the="" arithmetic="" sequence="" {1,="" 6,="" 11,="" 16,="" .="" .="" .}.="" 15.="" write="" the="" nth="" term="" formula="" for="" the="" geometric="" sequence="" {3,="" 6,="" 12,="" 24,="" .="" .="" .}.="" 16.="" find="" the="" sum="" of="" the="" first="" 30="" terms="" of="" the="" sequence="" {�1,="" 2,�4,="" 8,="" .="" .="" .}.="" 17.="" find="" the="" sum="" of="" the="" infinite="" geometric="" series,="" if="" possible:="" (a)="" 1x="" n="1" 4="" ✓="" 1="" 2="" ◆n�1="" (b)="" 2="" +="" 8="" +="" 32="" +="" 128="" +="" .="" .="" .="" 18.="" use="" the="" binomial="" theorem="" to="" expand="" (2x3="" �="" y)4.="" 19.="" find="" an="" equation="" for="" the="" parabola="" with="" directrix="" at="" x="3" and="" focus="" (�1,�1).="" find="" the="" two="" latus="" rectum="" points="" and="" graph="" the="" parabola="" labeling="" all="" important="" points.="" 20.="" find="" the="" center,="" major="" axis,="" vertices,="" and="" foci="" of="" the="" ellipse="" 3x2="" +4y2="" �="" 12x+8y+4="0." graph="" by="" hand="" and="" label.="" list="" answers="" as="" exact="" values,="" not="" decimal="">