113-rosay-07sp03-v3

# 113-rosay-07sp03-v3 - Math 113 EXAM 111 April 26th 2007(50...

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Unformatted text preview: Math 113 EXAM 111, April 26th, 2007, (50 minutes). NAME: SECTION: Instructor: TO RECEIVE CREDIT FOR AN ANSWER, YOU MUST SHOW WORK JUSTIFYING THAT ANSWER. I. (NO CALCULATOR, and do not forget to provide full justiﬁcation) (25 points) Find an angle oz such that: cos2 a z: 1 ~ sin2 10° and 900 < a < 180° . II. ' V (30 points) Find the weight W and the angleo’x in order that the ﬁgure shows an equilibrium. 111. No CALCULATOR. - (25 points) Let (7 =<-\,3> and V :<5 ,1>. On the ﬁgure, show the vectors (7, l7, (7+7, and 17— Evaluate the lengths, } and of the vectors (7 and K7, and evaluate the dot product (7 ‘ i7.. ' Give the EXACT value of the cosine of the angle a between the vectors [7 and l7 (geometric angle in the range from 0° to 180°, with no orientation taken into account). Without calculator can you say whether this is an acute or an obtuse angle? IV. (25 points) Let 2 and 2’ be the complex numbers 2 =—|+3i and z’ :5 +1i. Evaluate z + z’, 22’ and :7 in Cartesian form (i.e. a+bi)._ If {T : r(cos¢9 + isinO) is the writing of :7 in polar (Le. trigonometric) form, with r > 0 and —7r < 9 3 7r, give the EXACT values for r, c056 and sin6’. No Calculator, you are not asked the exact value of 9. On the ﬁgure of Problem III, Show the angle 6 with its orientation. Using your calculator, give an approximate value of 0 (in radians). - // .... -—ANSWERS---—-—-—---- / 2+z’: 22: r: ‘ ,00362 ,sin9: 6 2 radians. V. Prove that the following ﬁgure is not possible: (15» points) ...
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113-rosay-07sp03-v3 - Math 113 EXAM 111 April 26th 2007(50...

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