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MATH 1330 Final Exam Review 1. Evaluate the following expression: sin 37π 6 πππ π‘ππ 5π 31π β 3 2. Let P(x,y) denote the point where the terminal side of an angle π meets the unit circle. If P is in 2 Quadrant IV and π₯ = find sin π and tan π. 7 3. Given the following: π 0 < π₯ < , 0 < π¦ < π , sin π₯ = cos π¦ = Evaluate: cos(π₯ β π¦) 5 8 2 2 5 , 4. Evaluate:sin 330ο° β cos 120ο° 5. Give all possible polar coordinates for the point β5 , β5 given in rectangular coordinates. (In the choices below, n represents any integer.) 6. Simplify: sin(π₯) 1βcos(π₯) + 1βcos(π₯) sin(π₯) 7. Given π π₯ = 2 csc 5π₯ . Find the vertical asymptotes for f(x). 8. Find the exact value of the expression: β1 β4 tan sin 5 9. Given βπ΄π΅πΆ with β π΄ = 120ο° , β π΅ = 30ο° , and BC = 8 cm. Find AC. (All answers are in cm.) 2π₯ 10. Let π π₯ = ln π₯ and π π₯ = π . Find πβπ 7 . 11. A string running from the ground to the top of a fence has an angle of elevation of 60°. The fence is 6 feet tall. What is the length of the string? 12. State the coordinates of the focus for the 2 given parabola. π¦ β 2π₯ + 2π¦ β 13 = 0 13. Solve the following equation over the interval 2π [0, ]: 4 sin 5π₯ + 2 = 4 5 14. Evaluate the following expression: β1 1 sin + cos β1 β1 + tanβ1 (β 3 ) 2 15. Find the magnitude: v = 2 i ο 5 j 18. State the coordinates of the vertices for the π₯2 π¦2 given ellipse. + =1 36 49 19. Write the equation 2 2 2π₯ + 2 π¦ β 6 = 72 to polar coordinates. 20. Give tan π₯ = β3 and 0 < π₯ < π: find the value for sin 2π₯ . 21. Given vectors: u = < 6, ο 8>, v = < 4, 5 > , find u·v. 22. Given vectors: u = < 2, ο 3>, v = < ο7, 5 > , 3u β 2v 23. Find a sine function with positive vertical displacement satisfying : The amplitude is ½ , the π horizontal shift is units to the left, the vertical 3 π shift is 3 units up and the period . 9 24. Solve the following equation on the interval [0, 2π). 4π ππ2 π₯ β 3 = 0 25. Triangle ABC has sides measuring 3 in, 7in, and 9 in. Determine the value of cos A, where A is the largest angle.