01spfin - rmATHlIS swarm: 20m —Ros~1 4 . FWM __ ’7 Math...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: rmATHlIS swarm: 20m —Ros~1 4 . FWM __ ’7 Math 113 FINAL EXAM, May 18, 2001, (2 hours). 5 NAME: SECTION: Instructor: I. On this figure, lOC’l = 4, and [OB I = 2, and the are AB is an arc of the circle of radius 2, with center at 0. Give the exact value of the angle 6 shown on the figure, in radians and in degrees. Evaluate, EXACTLY, the perimeter and the area of the shaded region. C radians = 0 . l area of shaded region 2 \ t perimeter = 1 Mug/unwananamnuwanwww mmj m4 mammmm Hymn-Mina”wwwmmpm mm“ II. Give EXACT values. cos(;8:) = sin(—‘8—”) III. Evaluate EXACTLY sin (tan'1(-—2) + IV Let y($) = Asin(B:c + C) + D, with A > 0. If‘the maximum value of y(:z:) is 5, and the minimum value is 4. What can youysay about the constants A , B , C, D ? If, additionally, you know that y(0) = 4.5, what else can you say? This is the graph of the cosine function. Evaluate the abscissae x1, $2, $3, 334, x5, x5, x7 and $8 shown on the figure. The answer is to be given in terms of 0 (0 shown on the figure) Which .73]- is equal to cos—1(cos 6)? Justify your answer. if“ f E i V. If there is aIWind of 55 mi/h, blowing from the SOuth, which compass heading should a plane, flying at 500 mi/h (speed relative to air), keep in order to go in the direction of 200 west of north? WMWMWVMMquuxr-wwffi, fly mmno a“, ‘ Wm WM , ,v t u m wwwmmwwn, «:mummmvmmfiwr'“InmeMnMA‘L-y mum.” D0 only one Of the two problems VI A a for both. VI A. Determine the angle a, so that this is an equilibrium assume no friction). VI B. You cannot get credit VI B. Let X = 4?. 75' an . d 2 2 25+ Evaluate the lengths of these vectors and their dot product. ' ~ Give the EXACT Value of the cosine of the angle between these two vectors. Is the angle aCUte 01‘ Obtuse (d0 not use your calculator)? Write 17.116 VeCtordX as the sum of a vector parallel (proportional) to Z, and a vector Perpendlclflar to 2- D0 not apply a memorized formula, justify your result. Answer t0 VI A7 Or to - n _ — _ _ _ _ _ _ ' ‘ ‘ ‘ ' ' r - - - — - — — _ _ VII. 1) Let z be the complex number 2 = 1 — 2‘. Write z in polar form (rem). Evaluate 28 and %, both in polar form, and in rectangular form. 2) Evaluate the square roots of (1 — i), in polar form and in rectangular form (you may use the result of problem II). ...
View Full Document

Page1 / 6

01spfin - rmATHlIS swarm: 20m —Ros~1 4 . FWM __ ’7 Math...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online