Math 1151 – Spring 2007 Final Exam Answer Key

Math 1151 – Spring 2007 Final Exam
Answer Key
Required Problems
1.
− 33
65
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2.
3.
cos θ = − 12
13 , tan θ = − 5
12
a) amplitude, A : 4 ; period, T : π ; phase shift,
b) y-intercept: ( 0, 0 ) ; x-intercepts:
see graph below
4. see solution set for proof
5.
θ = π 6 , 5π
6
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φ
ω : π
2
( k π 2 , 0 ) , where k is any integer ;
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6.
a)
( x − 2 ) 2
6
+ ( y + 1 )2
3
= 1
b) center: ( 2, −1 ) ; vertices: ( 2 ± √6 , −1 ) ; foci: ( 2 ± √3 , −1 )
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c) see graph below
7. zeroes of the polynomial: 1 ,
− 9 2 + 3
2 i , − 9 2 − 3
2 i
Elective Problems
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8. a ≈ 5.43 , c ≈ 4.42 , β = 60º
9. zeroes of the polynomial: −3 , −2 ,
1
2 + 3
2 i , 1
2 − 3
2 i
10.
( 3 + i ) 7 = − 64 3 − 64 i
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11.
a) vertex: ( 2, -2 ) ; focus:
b) see graph below
( 2 , − 3 2 ) ; directrix:
y = − 5 2
12.
x = 1 3 , y = − 1 6€
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13.
cos (α + β ) = 3 − 4 3
10
14. see graph below
, sin (α + β ) = 4 + 3 3
10
graph for #3b

graph for #6c
graph for #11b

graph for #14
edges are included as part of the solution region for the inequality