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MAT 112-002
NAME:______KEY_____________
Take-Home Quiz 1
Score:___20_____
DUE DATE: Wednesday, September 14, 2005
1) Consider the following polynomial:
f ( x)  2 x6  11x5  40 x 4  81x3  56 x 2  14 x  20
a) List all the possible rational roots of f(x).
p: ±1, 2, 4, 5, 10, 20
q: ± 1, 2
p/q: ± 1, 2, 4, 5, 10, 20, ½, 5/2
b) Find all the zeros (both real and complex) of f(x).
f(x) = (2x+1)(x-1)2(x-2)(x2-2x+10)
So, the roots are -1/2, 1, 2, and 1±3i (the last two come from using the quadratic
formula on the quadratic portion of f).
2) Write the equation of a polynomial with real coefficients having degree 4 and zeros of
-1, 2 and 2-i.
(x+1)(x-2)[x-(2-i)][x-(2+i)] = (x2-x-2)(x2-4x+5) = x4-5x3+7x2+3x-10
3) Convert the following angles into degrees:

10
(π/10)(180/π) = 18○
a)
3
20
c)
2
3
(3π/2)(180/π) = 270○
(20π/3)(180/π) = 1200○
b)
4) Convert the following from DMS into decimal degrees (round to 4 decimal places):
a) 12 1322
12+13(1/60)+22(1/3600) = 12.2228○
b) 32 4510
32+45(1/60)+10(1/3600) = 32.7528○
5) Given that the acute angle θ has tan  
12
, find the values of the remaining 5
5
trigonometric functions.
sin θ = 12/13
cos θ = 5/13
tan θ = 12/5
csc θ = 13/12
sec θ = 13/5
cot θ = 5/12
6) Find the exact value of the following expressions:
a) tan 2 5  csc2 85
= tan2 5○ – sec2 (90○ – 5○)
= tan2 5○ – sec2 5○
= tan2 5○ – (tan2 5○ + 1 )
= -1

cos

5
3
cos
10
= cot (π/5) – cos (π/5) / sin (π/2 – 3π/10)
= cot (π/5) – cos (π/5) / sin (π/5)
= cot (π/5) – cot (π/5)
=0
b) cot
5

7) Find the exact value of the following expressions:

a) 4  tan 2
3
2
= 4 + (√3) = 4+3 = 7
b) 1  tan 2 30  csc2 45
= 1 + (1/√3)2 – (√2)2 = 1 + 1/3 – 2 = -2/3
8) Use a calculator to evaluate the following (round to 4 decimal places):
a) tan 20
0.36397
b) sec

7
1.10992
c) csc14
1.00948