This preview shows pages 1–6. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 ...
View
Full
Document
This note was uploaded on 08/08/2008 for the course MATH 113 taught by Professor Rosay during the Spring '07 term at Wisconsin.
 Spring '07
 ROSAY
 Trigonometry

Click to edit the document details