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Trig. > The 6 Trigonometric Functions. > Flashcards

The 6 Trigonometric Functions. Flashcards

1
Q

If Theta = 0 degrees, Sin Theta =

A

0

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2
Q

If Theta = 0 degrees, Cos Theta=

A

1

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3
Q

If Theta = 0 degrees, Tan Theta=

A

0

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4
Q

If Theta = PI/2 or 90 degrees, Sin 90 degrees=

A

1

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5
Q

If Theta = PI/2 or 90 degrees, Cos 90 degrees=

A

0

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6
Q

If Theta = PI/2 or 90 degrees, Tan 90 degrees=

A

Undefined.

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7
Q

If Theta = PI or 180 degrees, Sin 180 degrees=

A

0

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8
Q

If Theta = PI or 180 degrees, Cos 180 degrees=

A

-1

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9
Q

If Theta = PI or 180 degrees, Tan 180 degrees=

A

0

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10
Q

If Theta = PI/4 or 45 degrees, Sin 45 degrees=

A

Root 2/2

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11
Q

If Theta = PI/4 or 45 degrees, Cos 45 degrees=

A

Root 2/2

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12
Q

If Theta = PI/4 or 45 degrees, Tan 45 degrees=

A

1

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13
Q

If Theta = PI/6 or 30 degrees, Sin 30 degrees=

A

1/2

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14
Q

If Theta = PI/6 or 30 degrees, Cos 30 degrees=

A

Root 3/2

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15
Q

If Theta = PI/6 or 30 degrees, Tan 30 degrees=

A

1/Root 3

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16
Q

If Theta = PI/3 or 60 degrees, Sin 60 degrees=

A

Root 3/2

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17
Q

If Theta = PI/3 or 60 degrees, Cos 60 degrees=

A

1/2

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18
Q

If Theta = PI/3 or 60 degrees, Tan 60 degrees=

A

Root 3

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19
Q

1 degree=

A

pi/180 radians

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20
Q

1 radian=

A

180/pi

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21
Q

Arc Length=

A

s=r theta

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22
Q

Area of a sector=

A

A=1/2 r (squared) theta.

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23
Q

Sin Theta=

A

y

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24
Q

Cos Theta=

A

x

25
Q

Tan Theta=

A

y/x

26
Q

Cosec Theta=

A

1/y

27
Q

Sec Theta=

A

1/x

28
Q

Cot Theta

A

x/y

29
Q

What type of graph is this?

A

Sin

30
Q

What type of graph is this?

A

Cos

31
Q

What type of graph is this?

A

Cot

32
Q

What type of graph is this?

A

Cosec

33
Q

What type of graph is this?

A

Sec

34
Q

What type of graph is this?

A

Tan

35
Q

All Silver Tea Cups:

All is Quadrant I, _______ funtions are positive.

A

All!

36
Q

All Silver Tea Cups:

Silver is Quadrant II and _______ and _______ functions are positive.

A

Sin and Cosecant!

37
Q

All Silver Tea Cups:

Tea is Quadrant III and ______ and ______ functions are positive.

A

Tangent and Cotangent!

38
Q

All Silver Tea Cups:

Cups is Quadrant IV and _____ and ______ functions are positive.

A

Cosecant and Secant!

39
Q

What is the transformation?

y=f(x)+k

A

Vertically up by k units.

40
Q

What is the transformation?

y=f(x)-k

A

Vertically down by k units.

41
Q

What is the transformation?

y=f(x+h)

A

Horizontally left by h units.

42
Q

What is the transformation?

y=f(x-h)

A

Horizontally right by h units.

43
Q

What is the transformation?

y=f(x)

A

If a>1 vertically stretch.

If 0

44
Q

What is the transformation?

y=f(a*x)

A

If a >1, horizontally compress.

If 0

45
Q

What is the transformation?

y= -f(x)

A

Reflects about the x-axis.

46
Q

What is the transformation?

y= f(-x)

A

Reflects about the y-axis.

47
Q

In transformations, stretch=

A

Multiplication.

48
Q

In transformations, Compress=

A

Division.

49
Q

In transformations, Vertical=

A

On all y-coordinates.

50
Q

In transformations, horizontal=

A

on all the x-coordinates.

51
Q

Amplitude = I A I

A

All real numbers, no negatives.

52
Q

Period =

A

T= 2pi/w

53
Q

y=A sin w x

A

y=A cos w x

54
Q

State the domain, range and period of a sin function f(x)=sin(x).

A

Domain= ARN

Range= [-1,1]

Period=2pi

55
Q

State the domain, range and period of a cos function f(x)=cos(x).

A

Domain= ARN

Range= [-1,1]

Period=2pi

56
Q

State the domain, range, period and vertical asymptootes of a tan function f(x)=tan(x).

A

Domain=all real numbers except pi/2 + k pi, k is an integer.

Range=ARN

Period=pi

Vertical asymptotes: x = pi/2 + k pi, where k is an integer.

57
Q

State the domain, range, period and vertical asymptotes of a cot function f(x)=cot(x).

A

Domain: all real numbers except k pi, k is an integer.

Range: all real numbers

Period = pi

Vertical asymptotes: x = k pi, where k is an integer.

58
Q

State the domain, range, period and vertical asymptotes of a sec function f(x)=sec(x).

A

Domain: all real numbers except pi/2 + k pi, n is an integer.

Range: (-infinity , -1] U [1 , +infinity)

Period = 2 pi

Vertical asymptotes: x = pi/2 + k pi, where k is an integer.

59
Q

State the domain, range, period and vertical asymptotes of a csc function f(x)=csc(x).

A

Domain: all real numbers except k pi, k is an integer.

Range: (-infinity , -1] U [1 , +infinity)

Period = 2pi

Vertical asymptotes: x = k pi, where k is an integer.

Trig. (1 decks)

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