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Pre-Calculus Review 5.1 – 5.3 – Trigonometric Functions (A calculator is only allowed on #19 – 24) Name _______________________ Date __________ Period _______ 1.] Sketch the angle whose measure is 200 (in standard position). __________ 2.] What is the domain of the sine function? __________ 3.] What is the period of the cosecant function? __________ 4.] Express 175 in radians. Give answer in terms of . __________ 5.] Express 3 in degrees. 8 __________ 6.] If sin < 0 and tan >0, in which quadrant does the terminal side of lie? Identify the EXACT values of the 6 trig functions for each of the following. 7.] The terminal side of in standard position passes through (10, 24). sin cos = ______ tan = ______ sec = _____ cot = ______ 8.] 30 sin = ______ cos = ______ tan = ______ csc = ______ sec = ______ cot = ______ = ______ csc = ______ Determine the EXACT values for the following. __________ 9.] sin 11 4 __________ 10.] cos 495 __________ 12.] cos 2 273 __________ 11.] tan (-210) 1 csc 273 2 __________ 13.] tan (3 ) cot (183 ) Use the following information about angle to find the other trig functions. 7 14.] sin and is in quadrant IV. 25 csc = ______ __________ 15.] If cos = cos = ______ tan = ______ sec = ______ cot = ______ 2 find the EXACT value of sec( + 2). 5 __________ 16.] Given sin = 8 9 find the EXACT value of sin ( ). __________ 17.] Given cos = 13 , find sec ( - ). 17 __________ 18.] Given csc = 14 and is in Quadrant III, find the EXACT value of cot . 9 Calculator allowed problems (Be careful of what MODE you are in!) Round answers to 3 decimal places. __________ 19.] cot(64245) ? __________ 20.] sec 4 ? 9 __________ 21.] Find the arc length s, shown in the figure. 50 7 in __________22.] If the angle above measured s 7 , what would be the AREA of the sector? 9 __________ 23.] Find the distance between two cities, one directly north of the other, if one is located at latitude 60 22 '4" N, the other at latitude 7913' 25" N. (The radius of the earth is approximately 3960 miles.) __________ 24.] A bicycle tire has a radius of 1.5 feet. If in 4 seconds, the bicycle travels 400 feet, what is the tires angular speed? What is its linear speed? __________ Answers 1. 4. 35 36 5. 5 13 13 sec 5 12 13 7. 13 csc 12 sin 9. cos 2 2 10. 24 25 25 sec 24 cos 14. csc 17. 3. 2 2. Domain: (-∞,∞) 25 7 17 13 18. 135 2 or 67.5 6. III 12 5 5 cot 12 2 2 1 2 cos 3 2 csc 2 sec 2 3 3 sin tan 8. 11. 3 3 7 24 24 cot 7 12. 1 tan 115 9 19. 15. 8.497 5 2 22. 59.865 inches 2 23. 1303.222 miles 24. 66.667 rad sec 16. 100 ft sec 3 3 cot 3 13. 1 20. 5.759 21. 6.109 inches tan 8 9