376
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Chapter5
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AnalyticTrigonometry
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ln Exercises 1-6, verify that the x-values are solutions of the
equation.
2.
(b)x: 5r
TT
x:;
ln Exercises 33-38, find all solutions of the equation.
J
J
(b)r:T5r
,E
x:;
J
37.
tol ,-i_Tt
(b)
4.2cos24x-l:0
7t
(a) x:
16
5. 2sin2x
-
35. tan
I:0
3. 3tarf 2x -
sin;r
-
x: 5r
n
34.
sin2x: -
3x: I
36.
sec
38.
sin;: -*
I
*-D
cos-: --:22
4x:
t3
2
2
ln Exercises 39-42,find the x-intercepts of the graph.
39.
3n
(b)r:16
1
:i
33. cos r,
secx-2:0
1a)
3l,Zseczxltanzx-3:0
* sin xtanx:2
32. cosx
L.2cosx-1.:0
(a)
:::=-.
v: sin- *
"2
1
40. Y
:
sin n'x
+
cos
'''.x
:0
(b)x: 7r
TI
(a\ x:
-2
6
6.cscax-4csc2x:0
TT
x:
(a)
ft)x:
t)
5n
-
6
/
-'-\ I
\6/ vy
4l- .v:tunl!\
ln Exercises 7-20, solve the equation.
8.2sin;rt1:0
L0. tan x + 1Q: g
7.Zcosr*1:0
9.
',5cscx-2:0
11.3sec2*-+:O
13. sin x(sin -x + 1) :
14. (3
L5.
tan2
x
-
4cos2x-
12.3cot2x-1:0
:0
-
3)
-
:
0
16.
sin2x:
18. tan2 3x :
I7. 2 sinz 2x : |
19. tan 3x(tanx
1)
4
0
l)(tanz1;
L
/rx\
42. v: r..ol "o)42.y:seca[7/
:
3cos2x
ln Exercises 43 and 44, solve both equations. How do the
solutions of the algebraic equation compare with the
3
0
20. cos 2x(2 cos.r + 1) :
solutions of the trigonometric equation?
g
tn Exercises 21-32,find all solutions of the equation in the
43,6y2-13y+6:0
6cos2x- 13cosx*6:0
44.y,+y-20:0
sin2x * sinx - 20:0
lo,2z;-).
\
22. sec2r - 1 :0 \
2L. cos3 r : cos -x
24. 2sin2 x:2 * cosx
23. 3tan3 x: talx
.flq ln Erercises 45-54, use a graphing utility to approximate
26. sec.x csc r : 2 csc x
25.seczx-secx:2
the solutions of the equation in the interval l0,2tr\.
28. sec.r * tanx:
27. 2sinx * csc;r : 0
45.2sir.x * cosx:0
29.2cos2x*cosx-1:0
46. 4sin3 x * 2sin2x - 2 sinx - 1 : 0
30.2sin2x*3sinx*1:0
interval
1