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Z - AP Calculus > PRO Trig > Flashcards

PRO Trig Flashcards

1
Q

What function can be placed over one to get csc?

A

Sin

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2
Q

What function can be placed over one to get sec?

A

Cos

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3
Q

What function can be placed over one to get cot?

What functions can be placed over each other to get cot?

A

Tan, Cos/Sin

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4
Q

What function can be placed over one to get sin?

A

Csc

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5
Q

What function can be placed over one to get cos?

A

Sec

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6
Q

What function can be placed over one to get tan?

What functions can be placed over each other to get tan?

A

Cot, Sin/Cos

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7
Q

What is the first “Pythagorean” identity?

A

Sin^2 + Cos^2 = 1

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8
Q

How do you get the second and third “Pythagorean” identities?

A

Divide by Sin^2 and Cos^2

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9
Q

What are sin, cos, and tan in terms of x and y? (On the unit circle)

A

Sin=Y, Cos=x, and Tan=y/x

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10
Q

What is sin(-t)?

A

-Sin(t)

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11
Q

What is cos(-t)?

A

Cos(t)

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12
Q

What is tan(-t)?

A

-Tan(t)

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13
Q

What is sin(a+b)?

A

Sin(a)Cos(b) + Cos(a)Sin(b)

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14
Q

What is sin(a-b)?

A

Sin(a)Cos(b) - Cos(a)Sin(b)

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15
Q

What is cos(a+b)?

A

Cos(a)Cos(b) - Sin(a)*Sin(b)

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16
Q

What is cos(a-b)?

A

Cos(a)Cos(b) + Sin(a)*Sin(b)

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17
Q

What is tan(a+b)?

A

(Tan(a)+Tan(b))/(1-Tan(a)*Tan(b))

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18
Q

What is tan(a-b)?

A

(Tan(a)-Tan(b))/(1+Tan(a)*Tan(b))

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19
Q

What is Sin(2a)?

A

2Sin(a)Cos(a)

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20
Q

What is Cos(2a)?

A

Cos^2(a)-Sin^2(a), which you can use the first P identity to get 1-2Sin^2(a) or 2Cos(a)^2-1

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21
Q

What is Tan(2a)?

A

(2*Tan(a))/(1-Tan(a)^2)

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22
Q

What is Sin(a/2)?

A

+/- The square root of (1-Cos(a))/2

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23
Q

What is Cos(a/2)?

A

+/- The square root of (1+Cos(a))/2

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24
Q

What is Tan(a/2)?

A

+/- The square root of (1-Cos(a))/(1+Cos(a)) which is equal to (1-Cos(a))/Sin(a) or Sin(a)/(1+Cos(a))

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25
Q

What is Sin(x) + Sin(y)? (Might not need to know)

A

2Sin(x+y over 2)Cos(x-y over 2)

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26
Q

What is Sin(x) - Sin(y)? (Might not need to know)

A

2Sin(x-y over 2)Cos(x+y over 2)

27
Q

What is Cos(x) + Cos(y)? (Might not need to know)

A

2Cos(x-y over 2)Cos(x+y over 2)

28
Q

What is Cos(x) - Cos(y)? (Might not need to know)

A

-2Sin(x-y over 2)Sin(x+y over 2)

29
Q

What is Sin(x)*Cos(y)? (Might not need to know)

A

.5[Sin(x+y)+Sin(x-y)]

30
Q

What is Cos(x)*Sin(y)? (Might not need to know)

A

.5[Sin(x+y)-Sin(x-y)]

31
Q

What is Cos(x)*Cos(y)? (Might not need to know)

A

.5[Cos(x+y)+Cos(x-y)]

32
Q

What is Sin(x)*Sin(y)? (Might not need to know)

A

.5[Cos(x-y)-Cos(x+y)]

33
Q

What is the period of the normal sin and cos graphs?

A

2pie

34
Q

What is the period of tan and cot?

A

Pie

35
Q

What is the period of sec and csc?

A

2pie

36
Q

What is the amplitude of any trig function?

A

Tan, Cot, Sec, and Csc have no amplitude, the amplitude of sin and cos is the (absolute value of the) number in front of the function

37
Q

What is the formula for the period of a trig function?

A

regular period/the absolute value of the number inside the parenthesis of the function

38
Q

What is the phase shift of Trig(x+pie)?

A

Pie to the left

39
Q

What is the phase shift of Sin(Bx-C)?

A

C/B to the right

40
Q

What is the sin rule?

A

Sin(A)/a = Sin(B)/b = Sin(C)/c

41
Q

What is the cos rule?

A

The Opposite Side^2=Side^2 + Side^2 - 2sideside*Cos(angle)

42
Q

How do you find the area of a triangle using the sine rule?

A

1/2 * a * b * Sin(C)

43
Q

What is the point associated with 0*?

A

(1,0)

44
Q

What is the point associated with 30* or pie/6?

A

(Square root of 3 over 2, 1/2)

45
Q

What is the point associated with 45* or pie/4?

A

(Square root of 2 over 2, “”)

46
Q

What is the point associated with 60* or pie/3?

A

(1/2, Square root of 3 over 2)

47
Q

What is the phrase used with trig functions and right triangles?

A

SOH-CAH-TOA

48
Q

How do you convert between radians and degrees?

A

pie/180*

49
Q

What are the values of the sides of a 45* right triangle?

A

1,1,Square root of 2

50
Q

What are the values of the sides of a 30* right triangle?

A

1,2,Square root of 3

51
Q

What is Sin(90*-t)?

A

Cos(t)

52
Q

What is Tan(90*-t)?

A

Cot(t)

53
Q

What is Sec(90*-t)?

A

Csc(t)

54
Q

What is Cos(90*-t)?

A

Sin(t)

55
Q

What is Cot(90*-t)?

A

Tan(t)

56
Q

What is Csc(90*-t)?

A

Sec(t)

57
Q

What is Tan(30*)?

A

Square root of three over 3

58
Q

What is Tan(45*)?

A

1

59
Q

What is Tan(60*)?

A

Square root of three

60
Q

What Quadrants does Sin-1 need to be restricted to?

A

1 and 4

61
Q

What Quadrants does Cos-1 need to be restricted to?

A

1 and 2

62
Q

What Quadrants does Tan-1 need to be restricted to?

A

1 and 4

63
Q

What is the way to find out the area of a triangle given each side?

A

The square root of s(s-a)(s-b)*(s-c)

s=(a+b+c)/2

Z - AP Calculus (12 decks)

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