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MTH 120 - Summer 2005 Exam: Trigonometry and Algebra, Exams of Pre-Calculus

A summer 2005 exam for the mth 120 course at essex county college, focusing on trigonometry and algebra. The exam includes questions on evaluating trigonometric functions, finding expressions and sums, vector operations, infinite geometric series, trigonometric identities, and using the binomial theorem. Students are required to show all work and justify answers algebraically.

Typology: Exams

Pre 2010

Uploaded on 08/08/2009

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MTH 120 Summer 2005
Essex County College Division of Mathematics
Test # 31 Created June 22, 2005
Name:
Signature:
Show all work clearly and in order, and box your final answers. Justify your answers alge-
braically whenever possible. You have at most 110 minutes2to take this 100 point exam. No
cellular phones allowed.
1. Use your calculator to evaluate the trigonometric function. Round your answers to three
decimal places.
(a) cos 1.206 1 points
(b) tan 7π
81 points
(c) cot 3.529 1 points
(d) csc (6.895) 1 points
(e) sec 60.001 1 points
(f) arcsin (0.645) 1 points
(g) arccos 0.777 1 points
(h) arctan (2.358) 1 points
1This document was prepared by Ron Bannon using L
A
T
E
X 2ε.
210:40 a.m. until 12:30 p.m..
1
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pf4
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MTH 120 — Summer — 2005 Essex County College — Division of Mathematics Test # 3^1 — Created June 22, 2005

Name:

Signature:

Show all work clearly and in order, and box your final answers. Justify your answers alge- braically whenever possible. You have at most 110 minutes^2 to take this 100 point exam. No cellular phones allowed.

  1. Use your calculator to evaluate the trigonometric function. Round your answers to three decimal places. (a) cos 1. 206 1 points

(b) tan

− 78 π

1 points

(c) cot 3. 529 1 points

(d) csc (− 6 .895) 1 points

(e) sec 60. 001 1 points

(f) arcsin (− 0 .645) 1 points

(g) arccos 0. 777 1 points

(h) arctan (− 2 .358) 1 points

(^1) This document was prepared by Ron Bannon using LATEX 2ε. (^2) 10:40 a.m. until 12:30 p.m..

  1. Write an expression for the nth^ term. 4 points

2 , 1 , 8 9

  1. Find the sum. 5 points ∑^70

n=

(2n − 1)

  1. Given u = 〈 1 , − 5 〉 , v = 〈 5 , − 3 〉 , w = 〈− 3 , − 6 〉 , find. (a) 5w + 3v 3 points

(b) w · v 3 points

(c) ‖u − w‖ 3 points

(d) The angle between v and u. 3 points

  1. Evaluate (exact values) all six trigonometric functions for x = − 315 ◦.

(a) sin x 2 points

(b) cos x 2 points

(c) tan x 2 points

(d) cot x 2 points

(e) sec x 2 points

(f) csc x 2 points

  1. If z = − 1 − 1 i, find the trigonometric form of z and z^9 , also find z^9 in standard form. 10 points
  1. If sin α = − 5 13

and cos β = − 3 5

with both α and β are in the third quadrant. Find the exact values of the following.

(a) sin

( (^) α 2

3 points

(b) cos

( (^) α 2

3 points

(c) tan

( (^) α 2

2 points

  1. Find all solutions. 10 points 2 cos^2 x + 3 sin x − 3 = 0