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Trigonometry Final Exam Practice Answers Fall 2004 11 Questions, some with multiple parts. Most answers will be worth 5 points each. Name 1. Solve the right triangle below. A = 28 b= 62.4 c= 70.7 c b 62 33.2 2. Assuming each angle given is in standard position, find the quadrant of its terminal side. a) 842 b) 12 5 II IV 3. Suppose = 42 is a central angle in a circle with radius of 14.2 meters. Recall that s = r (angle in radians) and A = ½ r2 (angle in radians) a) Find the length of the arc subtended by . 10.4 m b) Find the area of the circular sector formed by . 73.9 m2 4. Use a calculator to find each to four decimal places. a) sec(-4.578) b) sin(167.5) -7.4635 0.2164 5. Fill in the blanks in the following table using exact values. Reference Angle sin cos -1/2 11 -/6 3 6 2 45 225 2 2 2 2 tan 3 3 1 6. Find the exact values of x that satisfy the given condition. a) cos x = -1, 0 x 6 , 3, 5 (b) cos x = 0, - x 2 -/2, /2, 3/2 Page 1 of 3 Trigonometry Final Exam Practice Answers 7. Consider the equation y 3 2 cos( x ) . 2 a) What is the amplitude? 2 b) What is the period? 2 c) What is the phase shift? right /2 d) What is the vertical translation? down 3 e) Graph y 3 2 cos( x ) on the given axis, with –2 x 2. 2 f) What is the domain of the above graph? (-, ) g) What is the range of the above graph? [-5, -1] 8. What is the maximum value of y 10 4 cos(7 x 14 9. What is the minimum value of y 9 4 cos(8 x 3 3 )? )? -13 10. Simplify cot x cos x + sin x using the fundamental identities. csc(x) 11. Verify the following: a) sec2 x – sin2 x – cos2 x = tan2 x cos( A B ) tan A cot B b) cos A sin B c) sin( x y ) sin( x y ) 2 sin x cos y Page 2 of 3 Trigonometry Final Exam Practice Answers 12. Use appropriate identities to find cos 75o exactly. 6 2 4 13. Use appropriate identities to find sin 195o cos 15o exactly. -1/4 14. Find the exact real number values without using a calculator. a) arctan 3 b) cos –1 0 60 90 15. Find exact solutions of 2 cos 2 + 3 sin = 0, 0o < 360o 210, 330 16. Solve the triangle with a = 28, b = 32, and c = 22. Give answers to two significant digits. A = 59 , B = 78 , C = 43 17. Change (-6, 30) to exact rectangular coordinates. ( 3 3 ,3 ) 18. Change (5 2 ,5 2 ) to exact polar coordinates. (10, -45) 19. Change 2 2i 3 to exact trigonometric form. 4cis120 20. Change to polar form (solve for r): x2=8y. 8 sin 8 tan r= or r = 2 cos cos 21. Change to rectangular form: r = 3sec(). x=3 22. For the vectors u = -5,3 and v = 4, -6, find the following: a) u + v -1, -3 b) 3u – 2v -23, 21 c) –7v 35, -21 d) the angle between u and v = 154.65 Page 3 of 3