Exam 3 Review Flashcards

Memorize what's necessary

1
Q

What is sin(theta) also equal to?

A

1/csc(theta)

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2
Q

What is cos(theta) also equal to?

A

1/sec(theta)

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3
Q

What is tan(theta) also equal to?

A

1/cot(theta)

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4
Q

What is csc(theta) also equal to?

A

1/sin(theta)

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5
Q

what is sec(theta) also equal to?

A

1/cos(theta)

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6
Q

what is cot(theta) also equal to?

A

1/tan(theta)

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7
Q

What is the fundamental Pythagorean identity?

A

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

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8
Q

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

A

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

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9
Q

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

A

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

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10
Q

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

A

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

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11
Q

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

A

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

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12
Q

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

A

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

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13
Q

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

A

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

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14
Q

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

A

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

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15
Q

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

A

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

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16
Q

What is the formula for converting from radians to degrees?

A

Radians = 180/pi degrees

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17
Q

What is the formula for converting from degrees to radians?

A

Degrees = pi/180

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18
Q

What is the formula for arc length?

A

S = r*theta

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19
Q

How do you find the linear velocity of a circle?

A

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

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20
Q

What is the even identity for cosine?

A

cos(−x)= cos(x)

21
Q

What is the odd identity for sine?

A

sin(−x)= −sin(x)

22
Q

What is the odd identity for tangent?

A

tan(−x)= −tan(x)

23
Q

What is the even identity for secant?

A

sec(−x)= sec(x)

23
Q

What is the odd identity for cosecant?

A

csc(−x)= −csc(x)

23
What is the sum identity for sine?
sin(A+B) =sin(A)cos(B)+cos(A)sin(B)
23
What is the odd identity for cotangent?
cot(−x)= −cot(x)
23
What is the sum identity for tangent?
tan(A+B) =tan(A)+tan(B)/1−tan(A)tan(B) ​
24
What is the difference identity for sine?
sin(A−B) =sin(A)cos(B)−cos(A)sin(B)
24
What is the sum identity for cosine?
cos(A+B) =cos(A)cos(B)−sin(A)sin(B)
24
What is the difference identity for cosine?
cos(A−B) =cos(A)cos(B)+sin(A)sin(B)
25
What is the difference identity for tangent?
tan(A−B) =tan(A)-tan(B)/1+tan(A)tan(B)
26
What is the double-angle identity for sine?
sin(2x) =2sin(x)cos(x)
27
What is the double-angle identity for cosine?
cos(2x) =cos^2(x)-sin^2(x), cos(2x) =2cos^2(x)-1, 1-2sin^2(x)
28
What is the double-angle identity for tangent?
tan(2x) =2tan(x)/1−tan^2(x)
29
What is the power-reduction identity for sin^2(x)?
sin^2(x)= 1−cos(2x)/2​
30
What is the power-reduction identity for cos^2(x)?
cos^2(x) =1+cos(2x)/2
31
What is the power-reduction identity for tan^2(x)?
1−cos(2x)/1+cos(2x)
32
What is the domain and range of sin(x)?
D: (-infinity,infinity) R:[-1,1]
33
What is the domain and range of cos(x)?
D:(-infinity,infinity) R:[-1,1]
34
What is the domain and range of tan(x)?
D:{t|t=\ pi/2 + pik} R:(-infinity,infinity)
35
What is the domain and range of csc(x)?
D:{t|t=\ pik, k any integer} R:(-infinity,-1]U[1,infinity)
36
What is the domain and range of sec(x)?
D:{t=\ pi/2+pik, k is any integer} R:(-infinity,-1]U[1,infinity)
37
What is the domain and range of cot(x)?
D:{t=\ kpi, k is any integer} R:(-infinity,inifinity)
38
What is the domain and range of arcsin(x)?
D:[-1,1] R:[-pi/2,pi/2]
39
What is the domain and range of arccos(x)?
D:[-1,1] R:[0,pi]
40
What is the domain and range of arctan(x)?
D:(-infinity,infinity) R:(-pi/2,pi/2)
41
What is the domain and range of arccsc(x)?
D:(-inifinity,-1]U[1,infinity) R:[-pi/2,pi/2],y=\0
42
What is the domain and range of arcsec(x)?
D:(-infinity,-1]U[1,infinity) R:[0,pi],y=\pi/2
43
What is the domain and range of arccot(x)?
D:(-infinity,infinity) R:(0,pi)