©Zarestky
Math 151 Quiz 1 Version B
1/25/2010
NAME:______KEY__________________________________
Section (Circle One):
1.
507
(3 pts) If tan x = !
If tan x = !
sin
508
509
510
511
512
3
3!
and
! x ! 2! , find the values of the other trig functions evaluated at x.
3
2
3
11!
, then x =
.
3
6
11!
3
11! 2 3
11!
1
4!
11!
=
=
, cot
, csc
= ! , cos
= ! 3 , sec
= !2
6
2
6
3
6
2
3
6
Partial credit:
Part 1) 0.5 pts for identifying the correct angle.
Part 2) 0.5 pts for correctly evaluating each of the 5 remaining trig functions. Give credit for the trig
functions if they match Part 1, even if Part 1 is incorrect.
2.
(2 pts) Solve the equation cos x = cot x for x, where 0 ! x ! 2! .
cos x
sin x
cos x sin x = cos x
cos x sin x !cos x = 0
cos x =
cos x(sin x !1) = 0
cos x = 0 or
! 3!
x= ,
2 2
sin x = 1
Partial credit:
Part 1) 1 pt for correct algebra. OK to skip steps.
Part 2) 1 pt for correct values of x. (0.5 pts for 1 correct value.)
3.
(2 pts) Find a unit vector in the direction of !2,7 .
!2,7 =
(!2)
The unit vector is
2
+ 7 2 = 53
!2,7
53
= !
2 53 7 53
,
53
53
Partial credit:
Part 1) 1 pt for correct magnitude.
Part 2) 1 pt for correct unit vector. (Full credit even if denominator is not rationalized.)
©Zarestky
4.
Math 151 Quiz 1 Version B
(3 pts) If a = !1,4 , b = 1,2 , and c = 5,0 , find scalars t and w such that ta + wb = c.
Use vector operations:
t !1,4 + w 1,2 = 5,0
!t,4t + w,2w = 5,0
!t + w,4t + 2w = 5,0
Identify and solve the corresponding system of equations:
!t + w = 5
5
10
gives t = ! , w =
4t + 2w = 0
3
3
Partial credit:
Part 1) 1 pt for correct set-up and algebra.
Part 2) 1 pt for correct system of equations and solution.
Part 3) 1 pt for correct values of t and w. (0.5 each)
1/25/2010