113-rosay-07sp03-v1

# 113-rosay-07sp03-v1 - Math 113 EXAM III, April 26th, 2007,...

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Unformatted text preview: Math 113 EXAM III, April 26th, 2007, (50 minutes). NAME: I SECTION: Instructor: TO RECEIVE CREDIT FOR AN ANSWER, ' YOU MUST SHOW WORK JUSTIFYIN G THAT ANSWER. I. (NO CALCULATOR, and do not forget to provide full justiﬁcation) (25 points) Find an angle oz such that: sin2 a 1 — c0527” and /80° < a <?_70 ° . II. _ (30 points) Find the weight W and the angle 6 in order that the ﬁgure shows an equilibrium. III. NO CALCULATOR. (25 points) Let (7 =<3,7> and V =<‘2,-—\>. On the ﬁgure, Show the vectors U, V, {7—H}: and V— U. Evaluate the lengths, and of the vectors (7 and- V, and evaluate the dot product (7‘ . ‘7. 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 =3 +7i and 2’ 22:1 . Evaluate 2 + 2’, '22:" and -:—, in Cartesian form (i.e. a+bi)."lf f: r(.cos6 + isin 6) is the writing of f in polar (i.e. trigonometric) form, with r > 0 and —7r < 6 3 7r, give the EXACT values for 7“, 0056 and sin 6. No Calculator, you are not asked the exact. value of 6. On the ﬁgure of Problem III, ' Show the angle 6 with its orientation. Using your calculator, give an approximate'value of 6 (in radians). — . ~ — “ANSWERS-"nun"— z+z'= - 22’: 1‘: « ,COSO: , )Sing: 6 :3 radians. V. Prove that the following ﬁgure is not possible: (15' points) 9 ...
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## This note was uploaded on 08/08/2008 for the course MATH 113 taught by Professor Rosay during the Spring '07 term at Wisconsin.

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113-rosay-07sp03-v1 - Math 113 EXAM III, April 26th, 2007,...

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