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Practice Test 2 Part B - Chapter 2 Sections 1,2,3 (11514717)
Question
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
Description This is the second of two practice tests for tests two. The other is Part A and covers 1.5, 1.6, 1.7 and 1.8
1.
Question Details
Fill in the blank to complete the trigonometric identity.
sec
2
-u
=
LarTrig9 2.1.004. [2548165] -
2.
Question Details
LarTrig9 2.1.008. [2446766] -
Use the given values to find the values (if possible) of all six trigonometric functions. (If an answer is undefined, enter UNDEFINED.)
csc
=
13 5
,
tan
=
5 12
sin =
cos =
tan =
csc =
sec =
cot =
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3.
Question Details
LarTrig9 2.1.009. [2446699] -
Use the given values to find the values (if possible) of all six trigonometric functions. (If an answer is undefined, enter UNDEFINED.)
cos
-x
2
=
20 29
,
cos
x
=
21 29
sin x =
cos x =
tan x =
csc x =
sec x =
cot x =
4.
Question Details
Match the trigonometric expression with one of the following. cot2 x - csc2 x
1 sec2 x + tan2 x sec2 x sin x tan x csc x
-1
LarTrig9 2.1.016. [2446984] -
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5.
Question Details
Match the trigonometric expression with one of the following. sec4 x - tan4 x
sin x tan x -1 sec2 x csc x
sec2 x + tan2 x 1
LarTrig9 2.1.017. [2446478] -
6.
Question Details
Match the trigonometric expression with one of the following.
sec2 x - 1 sin2 x
csc x
sec2 x + tan2 x 1
sin x tan x
-1 sec2 x
LarTrig9 2.1.019. [2446767] -
7.
Question Details
LarTrig9 2.1.021. [2446838] -
Factor the expression and use the fundamental identities to simplify. There is more than one correct form of the answer.
tan2 x - tan2 x sin2 x
8.
Question Details
LarTrig9 2.1.022. [2446942] -
Factor the expression and use the fundamental identities to simplify. There is more than one correct form of the answer.
6 sin2 x sec2 x - 6 sin2 x
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9.
Question Details
LarTrig9 2.1.025. [2548378] -
Factor the expression and use the fundamental identities to simplify. There is more than one correct form of the answer.
1 - 2 cos2 x + cos4 x
10.
Question Details
Factor the trigonometric expression. There is more than one correct form of the answer. 5 sin2 x - 14 sin x - 3
LarTrig9 2.1.029. [2446120] -
11.
Question Details
Factor the trigonometric expression. There is more than one correct form of the answer. 15 cos2 x + 22 cos x - 5
LarTrig9 2.1.030. [2447265] -
12.
Question Details
Factor the trigonometric expression. There is more than one correct form of the answer. cot2 x + csc x - 11
LarTrig9 2.1.031. [2446540] -
13.
Question Details
Factor the trigonometric expression. There is more than one correct form of the answer. sin2 x + 6 cos x + 6
LarTrig9 2.1.032. [2446811] -
14.
Question Details
LarTrig9 2.1.039. [2446174] -
Use the fundamental identities to simplify the expression. There is more than one correct form of the answer.
1 - cos2 x sec2 x - 1
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15.
Question Details
LarTrig9 2.1.042. [2446214] -
Use the fundamental identities to simplify the expression. There is more than one correct form of the answer.
cos2 y 1 - sin y
16.
Question Details
LarTrig9 2.1.045. [2446127] -
Perform the addition or subtraction and use the fundamental identities to simplify. There is more than one correct form of the answer.
1
7 + cos
x
+
7 1 - cos x
17.
Question Details
LarTrig9 2.1.046.MI. [2548230] -
Perform the subtraction and use the fundamental identities to simplify. There is more than one correct form of the answer.
2 sec x + 1
-
2 sec x - 1
18.
Question Details
LarTrig9 2.1.047. [2548206] -
Perform the subtraction and use the fundamental identities to simplify. There is more than one correct form of the answer.
tan x
-
sec2 x tan x
19.
Question Details
LarTrig9 2.1.048. [2548240] -
Perform the addition and use the fundamental identities to simplify. There is more than one correct form of the answer.
1
sin x + cos
x
+
1 + cos x sin x
20.
Question Details
Verify the identity. (Simplify at each step.) 8 cot2 y(sec2 y - 1) = 8
8 cot2 y(sec2 y - 1) = 8 cot2 y
= 8
LarTrig9 2.2.011. [2456916] -
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21.
Question Details
Verify the identity. (Simplify at each step.) 9 cos x + 9 sin x tan x = 9 sec x
9 cos x + 9 sin x tan x = 9 cos2 x +
cos x
= = 9 sec x
cos x
22.
Question Details
Verify the identity. (Simplify at each step.)
cot2 t 7 csc t
=
1 - sin2 7 sin t
t
cot2 t 7 csc t
=
cos2 t/
=
7/sin t cos2 t
=
1 - sin2 t 7 sin t
23.
Question Details
Verify the identity. (Simplify at each step.) sec x(csc x - 2 sin x) = cot x - tan x
sec x(csc x - 2 sin x)
=
1 cos x
1 sin x
-
2 sin2 x
=
1 cos x
1 - 2 sin2 x
1 - 2 sin2 x =
1 - (sin2 x + sin2 x) =
= sin x
cos2 x - sin 2 x
=
cos x sin x
-
sin x cos x
= cot x - tan x
LarTrig9 2.2.012. [2548256] LarTrig9 2.2.019. [2456731] LarTrig9 2.2.026. [2456740] -
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24.
Question Details
Verify the identity. (Simplify at each step.)
1
+ cos
sin
+
sin 1 + cos
=
2 csc
1 + cos sin
+
sin 1 + cos
=
sin (1 + cos )
2 + sin2
=
+ cos2 + sin2
sin (1 + cos )
2 + 2 =
sin (1 + cos )
2 =
=
2
sin
= 2 csc
sin (1 + cos )
25.
Question Details
Verify the identity. (Simplify at each step.)
cot - cot = 1
2
cot
-
2
cot =
1
=
= 1
cot cot
26.
Question Details
Verify the identity. (Simplify at each step.)
tan(sin-1 x) =
x 1 - x2
Let
= sin-1 x sin = x =
x 1
.
Thus,
tan(sin-1 x) = tan
=
1
1 - x2
1
x
=
1 - x2 .
LarTrig9 2.2.029. [2456521] -
LarTrig9 2.2.033. [2483728] LarTrig9 2.2.047. [2483687] -
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27.
Question Details
Verify the identity. 3 cos(sin-1 x) =
9 - 9x2
Let = sin-1 x
sin = x =
x 1
.
Thus,
3 cos(sin-1 x) = 3 cos
= 3 1- = 9 - 9x2
LarTrig9 2.2.048. [2548098] -
28.
Question Details
LarTrig9 2.3.011. [2446367] -
Solve the equation. (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians.)
2 csc x - 1 = 0 2
x =
29.
Question Details
LarTrig9 2.3.012.MI. [2548442] -
Solve the equation. (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians.)
tan x + 3 = 0
x =
30.
Question Details
LarTrig9 2.3.014. [2447279] -
Solve the equation. (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians.)
17 sin x + 8 = sin x
x =
31.
Question Details
LarTrig9 2.3.015. [2446651] -
Solve the equation. (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians.)
15 sec2 x - 20 = 0
x =
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