Download Math 8 CHAPTER 3 TEST SPRING 2010 Find the inverse function f

Math 8
CHAPTER 3 TEST
SPRING 2010
Find the inverse function f-1 of the function f. Find the domain of the function f and of its inverse function f-1.
(Make the answers clear)
1) f(x) = -6 cos(4x)
Find the exact value of the expression.
2) csc-1 - 2
Use a calculator to find the value of the expression in radian measure rounded to two decimal places.
10
3) cot-1 9
Find the exact value of the expression. Do not use a calculator.
6
4) tan-1 tan
7
tan-1 [tan (-
7
)] = -
7
Find the exact value, if any, of the composite function. If there is no value, say it is "not defined" and explain why it is
not defined. Do not use a calculator.
5) sin[sin-1 (1.6)]
undefined because sine is defined between -1 and 1 inclusive of both. 1.6 is out of this interval.
Find the exact value of the expression.
8
6) sec sin -1 9
7) cos tan -1
5
5
- csc-1
8
2
tan =
5
8
csc =
5
2
5 2 + 8 2 = r2
2 2 + x2 = 52
x2 = 25 - 4
25 + 64 = r
89 = r
cos
-
=
8
89
21
+
5
5 2
89 5
=
x = ± 21
8 21
10
8 21 + 10
+
=
·
5 89 5 89
5 89
1
89
8 1869 + 10 89
=
445
89
Find the exact value of the expression using a sum/difference formula AND a half angle formula.
8) cos
12
5
6
cos
1 + cos
=
2
5
6
2
1+ =
3
2
2
=
2- 3
2
=
2
2- 3
=
4
22
3
Use the information given about the angle , 0
2 , to find the exact value of the indicated trigonometric function.
3 3
< <2
Find sin .
9) sin = - ,
5
2
2
3
< <
4
2
1sin
2
=
4
5
2
=
5-4
5
2
=
1
10
=
10
10
Find the exact value of the expression.
tan 95° - tan (-25°)
= tan 95° - - 25° = tan 120° = 10)
1 + tan 95° tan (-25°)
3
Find the exact solution of the equation.
11) 7 cos-1 x - = 5 cos-1 x
2cos-1 x =
cos-1 x =
cos
2
2
=x
x=0
Find the real zeros of the trigonometric function on the interval 0
12) f(x) = 4 cos2 x - 3
0 = 4 cos2 x - 3
3
= cos2 x
4
3
= cos x
2
±
6
,
5
1
,
,
6
6
6
2
x<2
CHOOSE 3 OUT OF THE FOUR ONLY.
Solve the equation on the interval 0
2
=
13) cos 2 2
2
2 2 2
=
=
=
8
14)
4
=
=
,
=
2
8
4
2 -
+ 2k
2 -
+ 2k
4
8
+ 2k
4
=
<2 .
2
2k
2
=
+
8k
8
=
=
8
+
8
8
=
11
8
=
8
+ 2k
4
+ 2k
4
8
+ 2k
4
=
4
=
+
=
2
+
2k
2
+
8k
8
k= 0
8
+
8
8
=
3
9
11
,
,
8
8
8
3 tan 2
3 tan 2
= tan
- tan
=0
tan
3 tan - 1 = 0
tan = 0
3 tan - 1 = 0
= 0,
3 tan = 1
tan
=
0, ,
=
1
3
=
3
3
7
6 6
,
5
6 6
,
15) cos(2 ) = sin
1 - 2sin 2 = sin
0 = 2sin 2
0 = 2sin
2sin
2sin
sin
=
+ sin - 1
- 1 sin + 1
-1=0
=1
1
=
2
6
,
6
sin
sin
=
+1=0
= -1
3
2
6
,
6
,
3
2
3
17
8
=
8
+
16k
8
=
8
k= 1
16) sin
= - 2 - cos
sin
+ cos
= - 2
1
sin
2
+
1
cos
2
= -
2
sin
2
+
2
cos
2
= -1
cos sin + sin cos
sin +
= -1
sin
+
=
+
4
=
4
12 + 12 =
r=
2
2
cos
=
2
2
4
=
=
4
4
< 2 . Round the answer to two decimal places.
2
5
2
=
5
66.42°
1.16rad
360 - 66.42° 293.58°
2 - 1.16 5.12
CHOOSE 3 OUT OF THE 5 ONLY.
Establish the identity.
sin 3 - cos3
= 1 + sin cos
18)
sin - cos
sin - cos
sin 2 + sin cos
sin - cos
sin2 + sin cos
1 + sin cos
19)
2
2
= -1
Use a calculator to solve the equation on the interval 0
17) 2 sec = 5
5
sec =
2
cos-1
sin =
= -1
-
=
2
3
2
6
4
cos
1+ 1=
sin( - )
= cot
sin sin
+ cos2
=
=
= 1 + sin
cos
- cot
sin cos - cos sin
sin sin
=
cos
sin
-
=
cot
- cot
cos
sin
+ cos2
= cot
- cot
4
20) cos
cos2
x
x 2
- sin
= 1 - sin x
2
2
x
x
x
x
- 2cos sin + sin2
2
2
2
2
1 - sin 2
x
2
=
1 - sin x
21)
=
= 1 - sin x
sin(7 ) + sin(3 )
= cos(2 )
2 sin(5 )
2sin
7
+3
2
cos
2 sin(5 )
2sin
10
2
cos
2 sin(5 )
2sin
cos
2 sin(5 )
cos(2 )
4
2
7 -3
2
=
=
=
= cos(2 )
22) ln 1 + sin u + ln 1 - sin u = 2 ln cos u
ln 1 + sin u 1 - sin u
=
ln 1 - sin2 u
=
ln cos 2u
=
2 ln cos u
= 2 ln cos u
BONUS. YOU MUST COMPLETE THE ENTIRE TEST FIRST IN ORDER FOR THIS TO BE COUNTED.
Find the exact value of the expression. (10 POINTS)
12
23) cos 3 tan-1
5
5