Solution to Practice Exam for Trigonometry | MATH 1060, Exams of Trigonometry

Material Type: Exam; Class: Trig; Subject: Mathematics; University: University of Utah; Term: Fall 2007;

Typology: Exams

Pre 2010

Uploaded on 08/31/2009

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PRACTICE “EXAM 4”
This exam will cover 6.1-6.4 of the text, and material from each of the three previous exams
Math 1060-2, Fall 2007
For the following problems, refer to the notation on the oblique triangle shown below...
C
A B
a
c
b
1. Solve for all the unknown sides and angles of the given triangles:
(a) A= 24,B= 55,b= 3
(b) A= 100,a= 125, c= 10
(c) A= 110,a= 5, b= 8
(d) B= 63,b= 14, c= 13
(e) a= 55, b= 25, c= 72
(f) A= 55,b= 3, c= 10
2. Find the area of the triangle having the indicated angle and sides: B= 130,a= 62, c= 20
3. If ~
u=h−2,3iand ~
v=h1,2i, perform the following operations, and sketch (and label) the resultant vectors.
(a) ~
u+~
v
(b) ~
u~
v
(c) 2~
u
(d) 1
2~
v
(e) ~
u+ 3~
v
pf3
pf4

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PRACTICE “EXAM 4”

This exam will cover 6.1-6.4 of the text, and material from each of the three previous exams Math 1060-2, Fall 2007

  • For the following problems, refer to the notation on the oblique triangle shown below...

C

A B

a

c

b

  1. Solve for all the unknown sides and angles of the given triangles: (a) A = 24◦, B = 55◦, b = 3 (b) A = 100◦, a = 125, c = 10 (c) A = 110◦, a = 5, b = 8 (d) B = 63◦, b = 14, c = 13 (e) a = 55, b = 25, c = 72 (f) A = 55◦, b = 3, c = 10
  2. Find the area of the triangle having the indicated angle and sides: B = 130◦, a = 62, c = 20
  3. If ~u = 〈− 2 , 3 〉 and ~v = 〈 1 , 2 〉, perform the following operations, and sketch (and label) the resultant vectors. (a) ~u + ~v (b) ~u − ~v (c) − 2 ~u (d) 12 ~v (e) −~u + 3~v
  1. Given a vector in the plane with initial point (− 2 , −3) and terminal point (3, −1) (a) Find the component form of the vector (b) Find the magnitude of the vector (c) Find the direction angle of the vector
  2. Given the vector ~v = 5i + − 4 j (a) Find the component form of the vector (b) Find the magnitude of the vector (c) Find the direction angle of the vector
  3. Find a vector ~v in the direction of the unit vector ~u = 〈− √^318 , √^318 〉 that has magnitude ||~v|| = 6
  4. Find the vector ~v that has magnitude ||~v|| = 52 and direction angle θ = 35◦
  5. If ~u = 〈− 1 , 2 〉, ~v = 〈 2 , − 3 〉 and w~ = 〈 3 , 3 〉, perform the following operations involving the dot product (a) ~v · ~v (b) (~u · ~v)~w (c) (2w~ · 3 ~u)~v (d) (~u · ~v) − (~w · ~u)
  6. Find the angle between the two vectors (a) ~v = 〈 3 , 2 〉 and w~ = 〈 4 , 1 〉 (b) ~v = −i + 2j and w~ = 4i + j
  7. If ||~u|| = 4, ||~v|| = 12 and the angle between them is θ = π 3 , then find the dot product ~u · ~v
  8. Determine if ~v and w~ are orthogonal (a) ~v = 〈 3 , 5 〉 and w~ = 〈− 5 , 3 〉 (b) ~v = − 2 i + j and w~ = i + 12 j
  9. Find two vectors in opposite directions that are orthogonal to ~v = 〈− 1 , 32 〉
  10. Be sure you know how to do all the problems on the previous three exams.

Note: For your convenience, the following sheet of formulas and gigantic unit circle will be provided during the exam Remember: The FINAL EXAM is on TUESDAY, 12/11 from 8:30-10:30 p.m. in our REGULAR ROOM

GOOD LUCK WITH FINALS!!!

x

y

The Unit Circle