©Zarestky
Math 151 Quiz 1 Version A
1/25/2010
NAME:___KEY_____________________________________
Section (Circle One):
1.
507
508
509
(3 pts) If tan x = 3 and ! ! x !
If tan x = 3 , then x =
sin
510
511
512
3!
, find the values of the other trig functions evaluated at x.
2
4!
.
3
4!
3
4!
3
4!
2 3
4!
1
4!
=!
=
=!
, cos
, sec
= ! , cot
= !2 , csc
3
2
3
3
3
3
3
2
3
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 sin x = tan x for x, where 0 ! x ! 2! .
sin x
cos x
sin x cos x = sin x
sin x cos x !sin x = 0
sin x(cos x !1) = 0
sin x =
sin x = 0 or
x = 0,!,2!
cos 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 or 2 correct values.)
3.
(2 pts) Find a unit vector in the direction of 5,!2 .
5,!2 = 52 + (!2) = 29
2
The unit vector is
5,!2
29
=
5 29 2 29
,!
29
29
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 A
(3 pts) If a = 1,3 , b = 2,!1 , and c = 0,4 , find scalars t and w such that ta + wb = c.
Use vector operations:
t 1,3 + w 2,!1 = 0,4
t,3t + 2w,!w = 0,4
t + 2w,3t ! w = 0,4
Identify and solve the corresponding system of equations:
t + 2w = 0
8
4
gives t = , w = !
7
7
3t ! w = 4
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