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Trigonometry Review Solve all problems. Check your answers with the key provided after the questions. If you need help reviewing some topics, enroll in a section of TU 301 designated for use of the Math Center and get help at the Center. 1. Convert 21 4216 to decimal in degrees. 2. Convert 210 to radians. 3. Convert 4. If 60 is a central angle in a circle of radius 8 ft, find the length of the arc cut by and the area of the sector determined by the angle. 5. If (12, -5) is a point on the terminal side of an angle in standard position, find the exact values of the six trigonometric functions of . 6. Find the exact value of 7. Graph y 3 sin(2 x ) for one period. Label the axes appropriately. 8. Find the exact value of each expression. Do not use a calculator. 1 a. sin 1 2 7 to degrees. 4 1 b. cos 1 2 c. tan1 ( 3 ) 1 d. sin cos 1 3 sin(20 ) tan 200 . cos(380 ) 9. Use a calculator to find the value of each expression. Work in radians and round your answers to four decimal places. a. cos 1 ( 0.8) b. tan 1 (0.2) c. csc 1 (3) d. sin 1 (0.35) e. cot 1 (4) 10. 11. 7 Find the exact value of cos . 12 3 3 If sin , , find the exact value of sin . 5 2 2 12. Establish the identity sin( ) sin( ) 2 sin cos . 13. Solve the equation cos(2 ) 13. Solve the triangle having a 3, c 2, 110 . 14. Solve the triangle having a 2, b 3, 60 . 15. A ship, offshore from a vertical cliff known to be 100 feet in height, takes a sighting of the top of the cliff. If the angle of elevation is found to be 25 , how far offshore is the ship? 16. Find polar coordinates for the point with rectangular coordinates ( 3, 3 ) . 1 , 0 2 . 2 19. 2 Find the rectangular coordinates for the point with polar coordinates 5, 3 2 Plot the point given in polar coordinates. 3, 3 Plot the point given in polar coordinates. (2, 135 ) 20. Identify and graph the polar equation r = 3. 17. 18. Trigonometry Review KEY 1. 2. 3. 4. 5. 6. 7. 21.704 o 7 6 315o 8 32 2 s ft, A ft 3 3 5 12 5 12 13 13 sin , cos , tan , cot , sec , csc 13 13 12 5 12 5 0 2 2 2 (b) (c) (d) 3 3 6 3 9. (a) 2.4981 (b) 0.1974 (c) 0.3398 (d) 0.3576 (e) 0.2450 6 2 10. 4 3 3 10 or 11. 10 10 12. sin( ) sin( ) sin cos cos sin sin cos cos sin 2 sin cos 13. a 3, 42.972o , b 4.135, 110o , c 2, 27.028o 14. No such triangle 15. 214.451 ft 8. (a) 3 7 16. 6 , 2k or - 6 , 2k 4 4 5 5 3 17. , 2 2 18. 19. 20. Circle, center at (0, 0) and radius 3.