NAME Math 103 Exam 4 retake 12 December 2008 100 points Instructions 1 This exam has 7 pages including this one and the formula sheet which contain 7 questions and 2 bonus questions Please check that you have all of the pages 2 Answer all of the following questions clearly and completely Justify all of your answers 3 You may not use a book or any notes for this exam except the formula sheet attached as the last page of the exam 4 Give your answer to each problem completely and clearly in the space provided You may use the back of the exam pages for scratch work however if you want this work to be considered make note of it in the space provided for the problem 5 Erase or cross out work you do not wish to be graded 6 Credit partial or full will be given only if sufficient steps leading to the answers are shown 7 You have 50 minutes to complete this exam Page 1 Question 1 20 points Solve the following triangles A c b a 10 points b 4 c 5 B 95 B C b 10 points a 2 b 2 C 50 Page 2 a Question 2 20 points Find the exact values of the following expressions 7 4 a 5 points csc b 5 points cos 1 3 2 16 c 5 points tan 1 tan 9 d 5 points tan 3 8 Page 3 Question 3 20 points Consider the equation 4 sin2 1 4 a 10 points Find the general solution to this equation with no restriction on the value of b 10 points Find the solutions to this equation on the interval 0 2 Question 4 10 points Establish the identity csc 2 Page 4 1 sec csc 2 Question 5 10 points If tan 18 and is in Quadrant II then what are sin and cos 80 Question 6 10 points Let f x 4 sin 5 x What are the amplitude and the period of f Page 5 Question 7 10 points In the figure below the center of the circle is one of the corners of the triangle Find the area of the shaded triangle 5 in 4 in 7 in Bonus 3 points Explain why cos 1 cos 2 cos 3 cos 358 cos 359 1 Bonus 1 point Find a common English word containing the letters KSG together and in that order Page 6 Sum and difference formulas Sum to product formulas sin sin cos cos sin sin sin 2 sin sin sin cos cos sin cos cos cos sin sin cos cos cos sin sin tan tan tan 1 tan tan tan tan tan 1 tan tan Double angle formulas sin 2 2 sin cos cos 2 cos2 sin2 2 cos 2 1 2 sin cos 2 2 cos2 1 2 tan tan 2 1 tan2 Corollaries of double angle formulas 1 cos 2 2 1 cos 2 cos2 2 1 cos 2 tan2 1 cos 2 sin2 Half angle formulas r 1 cos sin 2 2 r 1 cos cos 2 2 r 1 cos tan 2 1 cos tan 1 cos sin 2 sin 1 cos Product to sum formulas 1 sin sin cos cos 2 1 cos cos cos cos 2 1 sin cos sin sin 2 cos 2 2 sin sin 2 sin cos 2 2 cos cos 2 cos cos 2 2 cos cos 2 sin sin 2 2 Law of Sines sin A sin B sin C a b c Law of Cosines c2 a2 b2 2ab cos C b2 a2 c2 2ac cos B a2 b2 c2 2bc cos A Area of a triangle In the following formulas K denotes the area of a triangle 1 bh 2 1 K ab sin C 2 1 K bc sin A 2 1 K ac sin B 2 p K s s a s b s c a b c where s 2 K