PDM 6.1
Pg. 353
2.
3.
4.
5.
x ≠ πk, for all int. k
All real numbers
t > 0
Pg. 325
2sinxsiny = cos(x – y) – cos (x + y)
13.
9. d
16a. y = 1
16b. t = 10
Pg. 294
b.
8b. Not an identity
Sample: Counterexample:
PDM 6.2
Pg. 358
1a. cot2x + 1
=
csc2x
1b. x ≠ πk, for all int. k
2.
cot2x + 1
=
csc2x
4a. x ≠ πk, for all int. k
4b.
PDM 6.2, pg 2
5.
Domain:
Domain:
7.
Domain:
PDM 6.2, pg 3
8.
Domain:
9.
= 1
= 1
= 1
= 1
12. x =-4, x = 5
Pg. 332
Pg. 314
18. x = ln 4,  1.386,
x = ln 2,  .6931
PDM 6.4
Pg. 370
10.
cos2   sin 2 
2. cos (x + y) = cosxcosy – sinxsiny
cos (x - y) = cosxcosy + sinxsiny
Pg. 354
5.
sinx
= sinx
21. C
Pg. 332
8.
sinx
9.
= sinx
2sinxsiny = cos(x - y) - cos (x + y)
= cosxcosy + sinxsiny - [cosxcosy - sinxsiny]
= cosxcosy + sinxsiny - cosxcosy + sinxsiny
Therefore, 2sinxsiny = 2sinxsiny
PDM 6.5
9a.
Pg. 375
1. sin(x + y) = sinxcosy + cosxsiny
sin(x - y) = sinxcosy – cosxsiny
Pg. 359
5.
Pg. 333
OR
tan x = ≈.291; cotx = ≈3.43
Or -1.15;
cscx = 2
22a. The decimal expansion of x is not
7.
8.
terminating and the decimal
expansion of x is not repeating.
22b. If the decimal expansion of x
is not terminating or repeating
then x is not a rational number.
22c. i - rational
ii - irrational
PDM 6.6
Domain:
Pg. 381
1.
Cos2x = 1 cos2x - sin2x
1- sin2x - sin2x
1 - 2sin2x
2sin2x
= 1 - 2sin2x
= 1 - 2sin2x
= 1 - 2sin2x
Cos2x = 1 - 2sin2x
2. Sin2x = 2sinxcosx
sin(x + x) = 2sinxcosx
sinxcosx + cosxinnx = 2sinxcosx
2sinxcosx = 2sinxcosx
2sinxcosx = 2sinxcosx
=
Pg. 333
24. 2x or 2x + 3
+
-
26a. 2x - 1
Pg. 401
10.
Pg. 371
16.
Pg. 375
1.sin(x + y) = sinxcosy + cosxsiny
sin(x - y) = sinxcosy – cosxsiny
PDM 6.7
Pg. 389
Pg. 381
2. Sin2x = 2sinxcosx
sin(x + x) = 2sinxcosx
sinxcosx + cosxsinx = 2sinxcosx
2sinxcosx = 2sinxcosx
2sinxcosx = 2sinxcosx
;
drawing
Pg. 376
0 –
-
PDM 6.8
Pg. 395
or
2.
13.
3.
4a. 0.841 and 5.442
b. 0.841 + 2πk, for all int. k
5.442 + 2πk, for all int. k
14.
5a.
=
5b.
6.
PDM 6.9
21.
Pg. 400
3

5
 2 k ,  2 k ,  2 k
2
4
4
or 1.04, 3.14, 5.23
b.
x

3
 2 korx 
32. secxcotx=cscx
5
 2 k , π + 2πk
3
Domain:
Domain:
36. secx + cotxcscx = secxcsc2x
14.
Pg. 401-03
8. 10. 15.
16. –
19.
Domain: