Exam 3 Review

Question 1

What is sin(theta) also equal to?

Answer 1

1/csc(theta)

Question 2

What is cos(theta) also equal to?

Answer 2

1/sec(theta)

Question 3

What is tan(theta) also equal to?

Answer 3

1/cot(theta)

Question 4

What is csc(theta) also equal to?

Answer 4

1/sin(theta)

Question 5

what is sec(theta) also equal to?

Answer 5

1/cos(theta)

Question 6

what is cot(theta) also equal to?

Answer 6

1/tan(theta)

Question 7

What is the fundamental Pythagorean identity?

Answer 7

sin^2(x)+cos^2(x)=1

Question 8

How can you express cos^2(x) in terms of sin^2(x)?

Answer 8

cos^2(x) = 1- sin^2(x)

Question 9

How can you express sin^2(x) in terms of cos^2(x)?

Answer 9

sin^2(x) = 1- cos^2(x)

Question 10

How can you express sec^2(x) in terms of tan^2(x)?

Answer 10

sec^2(x) = 1+ tan^2(x)

Question 11

How can you express csc^2(x) in terms of cot^2(x)?

Answer 11

csc^2(x) = 1+ cot^2(x)

Question 12

How can you express tan^2(x) in terms of sec^2(x)?

Answer 12

tan^2(x)= sec^2(x) - 1

Question 13

How can you express 1 in terms of tan^2(x) and sec^2(x)?

Answer 13

1= sec^2(x) - tan^2(x)

Question 14

How can you express cot^2(x) in terms of csc^2(x)?

Answer 14

cot^2(x)= csc^2(x) -1

Question 15

How can you express 1 in terms of csc^2(x) and cot^2(x)?

Answer 15

1= csc^2(x) - cot^2(x)

Question 16

What is the formula for converting from radians to degrees?

Answer 16

Radians = 180/pi degrees

Question 17

What is the formula for converting from degrees to radians?

Answer 17

Degrees = pi/180

Question 18

What is the formula for arc length?

Answer 18

S = r*theta

Question 19

How do you find the linear velocity of a circle?

Answer 19

You set velocity = to r*w and convert w with 2pi then balance the answer to the desired unit.

Question 20

What is the even identity for cosine?

Answer 20

cos(−x)= cos(x)

Question 21

What is the odd identity for sine?

Answer 21

sin(−x)= −sin(x)

Question 22

What is the odd identity for tangent?

Answer 22

tan(−x)= −tan(x)

Question 23

What is the even identity for secant?

Answer 23

sec(−x)= sec(x)

Question 23

What is the odd identity for cosecant?

Answer 23

csc(−x)= −csc(x)

Question 23

What is the sum identity for sine?

Answer 23

sin(A+B) =sin(A)cos(B)+cos(A)sin(B)

Question 23

What is the odd identity for cotangent?

Answer 23

cot(−x)= −cot(x)

Question 23

What is the sum identity for tangent?

Answer 23

tan(A+B) =tan(A)+tan(B)/1−tan(A)tan(B)
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Question 24

What is the difference identity for sine?

Answer 24

sin(A−B) =sin(A)cos(B)−cos(A)sin(B)

Question 24

What is the sum identity for cosine?

Answer 24

cos(A+B) =cos(A)cos(B)−sin(A)sin(B)

Question 24

What is the difference identity for cosine?

Answer 24

cos(A−B) =cos(A)cos(B)+sin(A)sin(B)

Question 25

What is the difference identity for tangent?

Answer 25

tan(A−B) =tan(A)-tan(B)/1+tan(A)tan(B)

Question 26

What is the double-angle identity for sine?

Answer 26

sin(2x) =2sin(x)cos(x)

Question 27

What is the double-angle identity for cosine?

Answer 27

cos(2x) =cos^2(x)-sin^2(x), cos(2x) =2cos^2(x)-1, 1-2sin^2(x)

Question 28

What is the double-angle identity for tangent?

Answer 28

tan(2x) =2tan(x)/1−tan^2(x)

Question 29

What is the power-reduction identity for sin^2(x)?

Answer 29

sin^2(x)= 1−cos(2x)/2​

Question 30

What is the power-reduction identity for cos^2(x)?

Answer 30

cos^2(x) =1+cos(2x)/2

Question 31

What is the power-reduction identity for tan^2(x)?

Answer 31

1−cos(2x)/1+cos(2x)

Question 32

What is the domain and range of sin(x)?

Answer 32

D: (-infinity,infinity) R:[-1,1]

Question 33

What is the domain and range of cos(x)?

Answer 33

D:(-infinity,infinity) R:[-1,1]

Question 34

What is the domain and range of tan(x)?

Answer 34

D:{t|t=\ pi/2 + pik} R:(-infinity,infinity)

Question 35

What is the domain and range of csc(x)?

Answer 35

D:{t|t=\ pik, k any integer} R:(-infinity,-1]U[1,infinity)

Question 36

What is the domain and range of sec(x)?

Answer 36

D:{t=\ pi/2+pik, k is any integer} R:(-infinity,-1]U[1,infinity)

Question 37

What is the domain and range of cot(x)?

Answer 37

D:{t=\ kpi, k is any integer} R:(-infinity,inifinity)

Question 38

What is the domain and range of arcsin(x)?

Answer 38

D:[-1,1] R:[-pi/2,pi/2]

Question 39

What is the domain and range of arccos(x)?

Answer 39

D:[-1,1] R:[0,pi]

Question 40

What is the domain and range of arctan(x)?

Answer 40

D:(-infinity,infinity) R:(-pi/2,pi/2)

Question 41

What is the domain and range of arccsc(x)?

Answer 41

D:(-inifinity,-1]U[1,infinity) R:[-pi/2,pi/2],y=\0

Question 42

What is the domain and range of arcsec(x)?

Answer 42

D:(-infinity,-1]U[1,infinity) R:[0,pi],y=\pi/2

Question 43

What is the domain and range of arccot(x)?

Answer 43

D:(-infinity,infinity) R:(0,pi)