Name Click here to enter text. This exam is worth 100 points. Questions 1 - 10 are each worth 4 points; do not show your work. Questions 11 - 20 are each worth 6 points; show your work to earn full credit. Write answers on the appropriate numbered blank. You can insert additional lines if needed. Leave answers in exact form unless otherwise directed to approximate the results. Write all fractions in lowest form. Round decimals to hundredths unless otherwise directed to round. Write answers using positive exponents except when using scientific notation. Simplify all radicals and rationalize the denominators. Write complex numbers in the form a + bi. Applied problems must have the variables identified (Let x =) and an equation for full credit. Select the letter of the one alternative that best completes the statement or answers the question. For multiple choice questions, check that the answers are all letters (A, B, C, D, or E) and not a value. 1.) Convert the 91.52 to degrees, minutes, and seconds. Round seconds to whole units, if necessary. 1.) _______ A) 9131'18'' 2.) B) 9131'12'' C) 9131'0'' D) 9131'52'' E) None of these From a balloon 892 feet high, the angle of depression to the ranger headquarters is 4526'. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)? 2.) _______ A) 869 ft 3.) B) 879 ft Find sin if cos = C) 874 ft 4 7 D) 884 ft E) None of these and in quadrant IV. Give an exact answer. 3.) _______ A) 4.) 33 4 B) 33 7 C) 7 4 D) 33 E) None of these Convert 165 to radian measure. Give an exact answer. A) 5 6 B) 11 12 C) 12 13 10 11 D 1 4.) _______ E) None of these 5.) A bicyclist's average linear speed during a race was 34 mph. His bicycle wheel has a 16-in. diameter. What was the angular speed of the wheel in revolutions per hour? Round to the nearest whole number. 5.) _______ A) 2 revolutions per hour B) 134,640 revolutions per hour C) 3571 revolutions per hour D) 42,857 revolutions per hour E) None of these 6.) Find the exact value of A) 7.) 9.) 10.) B) 6 C) Find the exact value of A) 8.) 3 B) 2 2 sin 1 ( 23 ) 7 6 ( 3 D) 1 tan cos C) in radians. 3 3 3 2 ) A) D) 5 , 6 6 B) E) None of these . D) Solve the equation for the interval [0, 2). 2 4 5 , , , 3 3 3 3 6.) _______ 7.) _______ 1 2 E) None of these 2 4 sin x1=0 5 7 11 , , , 6 6 6 6 C) 2 5 , , , 3 6 3 6 8.) _______ E) None of these Find a nonnegative angle less than 360 for cos = 0.3256, in (270 , 360). (Use calculator and fill in the blank.) 9.) _________ Solve triangle, if possible. If necessary, round your answers to the nearest tenth. 10.) ______ A) C = 103, a 16, b 9 C) C = 103, a 44.4, b 25.1 E) None of these B) C = 97, a 8.8, b 15.7 D) C = 103, a 9, b 16 2 SHORT ANSWER. Show your work. The following questions are each worth 6 points. 11.) Using Heron's Formula, find the area of the triangle with the following sides: a = 5 inches, b = 12 inches, and c = 13 inches. 11.) _____________ 12.) Solve the right triangle. a = 16.6, b = 21.8 Round answers to tenths. 13.) To find the distance AB across a river, a distance BC of 1083 m is laid off on one side of the river. It is found that B = 101.1 and 12.) ___________ ___________ ___________ C=16.4 . Find AB. Round to the nearest meter. 13.) _____________ 14.) Use trigonometric identities to find the exact value of sin 185 cos 65 - cos 185 sin 65. Give an exact answer. 14.) _____________ 15.) Find cos given that cos 2 = 5 6 and 0 < 2 . Give an exact answer. 15.) ____________ 16.) Prove: csc 2 sec 2 = 2 cot 2 c sc 2 17.) Prove: sin+tan =sin tan cot+ csc 18.) Solve the equation for the interval [0, 2). 4 sin2x = 4 cos x + 1 3 18.) _____________ 19.) 20.) Find the area of triangle. A = 30.2, b = 14.6 in., c = 6.8 in. Round to the nearest whole number. Solve, finding all solutions in [0, 2 Take answer out four places. 19.) _____________ ). 4 cos x + 1 = 4.268 20.) _____________ 4