11. Find the rational zeros using the rational zero theorem: y = (x+1)(x-4)(x+3)
Which means we have zeros (-1,0), (4,0) and (-3,0) and y-intercept (0, 12)
The graph is:
12. Asymptotes: x =6, x = -4
And y = 0
Ints: (8,0) & (1/3, 0)
13. Verify: (cosx + cosy)2 + (sinx - siny)2 = 2 + 2cos(x + y)
L = cos2x + 2cosxcosy + cos2y + sin2x – 2sinxsiny + sin2y
= 2 + 2cosxcosy - 2sinxsiny
= 2 + 2(cosxcosy – sinxsiny)
= 2 + 2 cos(x+y) = R
14. Verify:
L=
sin( 2 x)
= tan x
1  cos( 2 x)
2 sin x cos x
2 sin x cos x
2 sin x cos x
2 sin x cos x



 tan x = R
2
2
2
2
2
2
1  cos x  sin x (1  sin x)  cos x cos x  cos x
2 cos 2 x
15. Find the cube roots of -4 - 4 3 i.
Write the numbers in standard form (ie. a + bi).
First write the complex number in polar form: -4 - 4 3 i = 8cis(240)
Find the first root by raising this to the power
1
:
3
1
x1 = (8cis(240 )) 3 = 2cis(80)
360
= 120 and add this to the angle to obtain the remaining roots.
3
x2 = 2cis(200)
x3 = 2cis(320)
Then, find  =
Finally, let’s convert these to standard form:
x1 = 2cis(80) = 2cos(80) + 2isin(80)
 0.35 + 1.97
x2= 2cis(200) = 2cos(200) + 2isin(200)  -1.88 – 0.68i
x3= 2cis(320) = 2cos(320) + 2isin(320)  1.53 – 1.29i