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Math 180 - Trigonometry Review- Sections 5.1-5.3 Name___________________________________ Convert the angle to decimal degrees and round to the nearest hundredth of a degree. 1) 31e23'6'' 2) 295e6'24'' Convert the angle to degrees, minutes, and seconds. 3) 37.54e 4) 193.32e Convert the degree measurement to radians. Express answer as multiple of p. 5) 480e 6) - 144e Convert the angle in degrees to radians. Express the answer in decimal form, rounded to two decimal places. 7) 310e Convert the radian measure to degrees. (Round to the nearest hundredth when necessary) 8p 8) 7 9) 43 p 18 Convert the angle in radians to degrees. Round to two decimal places. 10) 4 In the problem, t is a real number and P=(x,y) is the point on the unit circle that corresponds to t. Find the exact value of the given trigonometric function. 5 11 11) , ; find sin t 6 6 12) - 21 2 , - ; find cot t 5 5 13) - 33 4 , ; find cos t 7 7 A point on the terminal side of angle q is given. Find the exact value of the given trigonometric function. 14) (12, 16); Find sin q. 15) (2, -3); Find sin q. 16) - 1 1 , ; Find cos q. 3 5 1 Give the exact value. 17) sec 30e Solve the problem. 18) Find the exact value of cos 60e + tan 60e. Do not use a calculator. 1+2 3 3 3 1+ 3 A) B) C) 2 2 2 19) Find the exact value of sin D) 2 3 p p - cos . Do not use a calculator. 3 6 Find the exact value of the expression. 20) csc 30e - cos 30e 21) sec 30e - sin 45e Find the exact value of the expression. Do not use a calculator. 14p 22) cos 3 23) sec 19p 4 24) sin 855e Solve the problem. 25) Find the exact value of tan 150e cos 210e. Do not use a calculator. Find the approximate value of the expression rounded to two decimal places. 26) sin 70e 27) tan 32e 28) cos 5p 12 29) sec p 5 30) cot p 7 Use the fact that the trigonometric functions are periodic to find the exact value of the expression. 10p 31) cos 3 32) sin 765e 33) tan 13p 4 2 Name the quadrant in which the angle q lies. 34) tan q > 0 and sin q < 0 35) sin q > 0 and cos q < 0 36) cos q > 0 and csc q < 0 37) sec q < 0 and tan q < 0 Use the given values of the sine and cosine to find the function value. 5 -2 6 38) sin q = - , cos q = . Find tan q. 7 7 39) sin q = - 5 2 6 , cos q = . Find csc q. 7 7 Find the exact value of the expression. 40) sec2 65e - tan2 65e 41) sin2 25e + cos 2 25e 42) sin 55e csc 55e Solve the problem. 43) Given sin q = A) cos q = C) cos q = - 1 and sec q < 0, find cos q and tan q. 2 3 1 , tan q = 2 3 3, tan q = - 10 3 B) cos q = - 3 1 , tan q = 2 3 D) cos q = - 3 1 , tan q = 2 3 Find the exact value of the requested trigonometric function of q. 2 44) cos q = and tan q < 0 5 Find sin q. 45) sec q = 9 and q in quadrant IV 8 Find tan q. 46) sin q = - 2 and tan q > 0 9 Find sec q. Use the even-odd properties to find the exact value of the expression. 47) cos (-60e) 48) csc - p 3 3 49) tan - p 3 50) sin (-60e) 4 Answer Key Testname: TRIG-REVIEW.TST 1) 2) 3) 4) 31.39e 295.11e 37e32'24'' 193e19'12'' 8p 5) 3 4p 5 6) 7) 8) 9) 10) 5.41 205.71e 430e 229.18e 11 11) 6 21 2 12) 33 7 13) 14) 4 5 15) - 3 13 13 16) - 5 34 34 17) 2 3 3 18) A 19) 0 4- 3 20) 2 21) 4 3-3 2 6 22) - 1 2 23) 2 2 24) 25) 26) 27) 28) 29) 30) 2 5 3 6 0.94 0.62 0.26 1.24 2.08 1 Answer Key Testname: TRIG-REVIEW.TST 1 2 31) - 2 2 32) 33) 34) 35) 36) 37) 1 Quadrant III Quadrant II Quadrant IV Quadrant II 5 6 38) 12 39) - 7 5 40) 1 41) 1 42) 1 43) B 44) - 21 5 45) - 17 8 46) - 9 77 77 47) 1 2 48) - 2 3 3 49) - 3 3 50) 2 2