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1 Exam Name ---_._ ~ '. Semester Exam - Trigonometry 2012 f ('0'<...<=--\-\( e. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the degree measure to radians. Leave answer as a multiple of if. 1) 330 1) _-'- A) 1171: 12 B) 11i1 6 C) 11i1 3 D) 1171: 5 Convert the radian measure to degrees. Round to the nearest hundredth if necessary. 2) 1071: 3 2) _ A) 601 B) C) 6000 D) Find the exact circular function value. 3) cot 71: A) 1 B) Undefined C)o D) -1 3) _ ) tan 771: 6 ) A),J3 2 C) -,J3 371: 5) see 5) _ A) -2 13) _ 2,J3 3 C)~ 2 D)-~ Use a table or a calculator to evaluate the function. 6) cos A) ) C) 1.01 D) ) _ 7) cot A) ) C).68 D) ) _ Find the value of s in the interval [0,71:/2] that makes the statement true. 8) eos s = A) ) 0, C) D) ) _ 9) cse s = A) ) C) D) ) _ Give the amplitude or period as requested. 10) Amplitude of y = - sin x 10) ---, A) 271: 13) C)~ D) -71: A-I

2 11) Period of y = sin 3x 11) _ A) 2n 13)~ 3 C)1 0) 3 Find the phase shift of the function. 12)y=sin[x+ ~l A).!!:... units to the right 71. d B) - umts own 12) C).!!:... units up O).!!:...units to the left 13) Y= 5 sin [x - ~ J A).!!:... units to the right 8 C) n units down B) 71 units to the left 2 0) 571 units up 13) Find the exact value of the real number y. 1) Y = sin-1 [f] 1) _ A)~ 3 C)71 3 B) ) Y= cot-1 (-1) 15) _ A) 3n B) 771 0) n Evaluate the function requested. \Vrite your answer as a fraction in lowest terms. 16) A 16) 50 0 B Find sin A. A) sin A =.! ) sin A =" C) sin A =.! 3 0) sina=l 5 17) From a boat on the lake, the angle of elevation to the top of a cliff is 29 38'. If the base of the cliff is 17) _ 655 feet from the boat, how high is the cliff (to the nearest foot)? A) 383 ft B) 373 ft C) 376 ft 0) 386 ft A-2

3 .ve the triangle. ~ 18) B = 3. C = 11.2 b = A) A = 29., a = 7.63, c = C) A = 31., a = 29.20, c = 9.63 S) A = 31., a = 27.20, c = 7.63 D) A = 29., a = 9.63, c = ) _ 19) To find the distance AB across a river, a distance BC = 1053 m is laid off on one side of the river. It 19) is found that B = and C = Find AS rounded to the nearest meter. A)309m B)353m C)306m D) 350 m Find the area of triangle ABC with the given parts. Round to the nearest whole number. 20) A = 26. b = 12.3 in. c= 7.7 in. 20) A) 19.1 in.2 B) 2. in.2 C) 21.1 in.2 D). in.2 21) Find the area of a triangular-shaped field with sides of 175. m and 226.7m, and the included angle 21) _ between them measuring Round to the nearest square meter. A) 39,068 m2 13)3702 m2 C) 703 m2 D) 19,53 m2 Find the missing parts of the triangle. 22) A = 30.0 a = 5.13 b = A) B = 60.0, C = 60.0, c = 8.89 C) B = 60.0, C = 90.0, c = 8.89 B) B = 90.0, C = 60.0, c = 8.89 D) no such triangle 22) 23) C = a = 7.50 km b = 9.80 km A) No triangle satisfies the given conditions. C) c = 20.6 km, A = 2.9,13 = )c = 17.7 km, A = 28.9, B = 3. D) c = 1.8 km, A = 26.9, B = ) 2) Two points A and B are on opposite sides of a building. ;\ surveyor chooses a third point C 77 yd 2) _ from Band 103 yd from A, with angle ACB measuring How far apart are A and B (to the nearest yard)? A) 91 yd B) 118 yd C) 109 yd D)100 yd Find the area of triangle ABC with the given parts. Round to the nearest whole number. 25) a = 17. cm b = 15.0 cm c = 13. cm 25) A) 106 cm2 13)103 cm2 C) 100 cm2 D) 97 cm2 A-3

4 I' /ti'dentities to find the exact value. 26) cos ) A) -J6 + -J2 U) --J6 --J2 tj q -J6 - -J2 D) -J2 - -J6 Find the exact value of the expression using the provided information. 27) Find cos(s + t) given that cos s =l,with s in quadrant 1,and sin t = _l, with t in quadrant IV. 27) 3 2 A) 2-J ) -J3 + 2-J2 q -J3-2-J2 D) 2-J Find the exact value by using a sum or difference identity. 28) tan 75 A) - -J3-2 13) -J3-2 q-j3+2 28) Use trigonometric identities to find the exact value. 29) sin 25 cas 35 + cas 25 sin 35 A) -J3 13) q-j3 3 D)l 2 29) Use an identity to write the expression as a single trigonometric function or as a single number. 30) 2 cos A)-J3 3 13) -J3 q-j2 f 30) Find the exact value by using a half-angle 31) sin 22.5 A)l~2 2 +-J2 identity. 31) Solve the equation for the interval [0, 2n). 32) cos2x + 2 cas x + 1 = 0 32) A) {2n} D) {n} 33) Solve the equation in the interval [0,360 ). 3) sin20 = 3 A) {60,120, 20, 300 } q {2LlO, 300 } 13) 0 D) (60, 120 ) 3) A-

5 / L"'the complex number in rectangular form. /", 35) 8(cos 9 + i sin 9 ) A) O.i 13) i C) O.i D) i 35) 36) Find the product. Write the product in rectangular form, using exact values. 37) [7(cos 60 + i sin 60 )] [2(cos 90 + i sin 90 )] A) 7--.]3-28 i 13) -1'h./3-1 i C) -7--.]3 + 7 i D) 2-]6 - -J2i 37) Find the following quotient, and write the quotient in rectangular form, using exact values. 38) 5(cas i sin 200 ) 38) (cas 50 + i sin 50 ) --- A) ]3 + 5 i B) - ~ + --.]3i C) ]3i D) l0--.j3i Find the given power. Write answer in rectangular form. 39) (1 - i)10 A) 32-32i B) 32 C) -32i D) i 39) Find all cube roots of the complex number. Leave answers in trigonometric form. 0) 6(cas i sin 291 ) A) cis 97, cis 217, cis 2170 C) cis 97, cis 217, cis 337" B) cis 187, cis 27, cis 127 D) cis 97, cis 157, cis 37 0) _ Give the rectangular coordinates for the point. 1) (1,270 ) AHO, 1) 13)(1,0) D) (0, -1) 1) 2) (6,225 ) A) (-3-J2, -3-J2) B) (-371, -371) 2) The rectangular coordinates of a point are given. Express the point in polar coordinates with r::: 0 and 0 ::: 8 < ) (,) 3) A) (,90 ) 13) (-J2,S0) C) (-J2, 13S0) D) (,5 ) ) (2, -2) A) (2-J2,5 ) ) A-5

6 AJ, :,wer Key Lestname: TRIG SEMESTER EXAM ) B 2) C 3) B ) B 5) 0 6) 0 7) C 8) C 9) A 10) B 11) B 12) 0 13) A 1) C 15) A 16) A 17) B 18) B 19) 0 20) C 21) 0 22) B 23) 0 2) A 25) 0 26) B 27) B 28) C 29) A 30) 0 31) C 32) D 33) B 3) A 35) 0 36) C 37) C 38) A 39) C 0) C 1) 0 2) A 3) B ) 0