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Practice Test 2 Part B - Chapter 2 Sections 1,2,3 (11514717)

Question

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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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