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Engineering Maths > Trigonometry > Flashcards

Trigonometry Flashcards

1
Q

State the three basic Trigonometric identities.

A
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2
Q

State the sine rule

A
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3
Q

Draw the cast diagram for degrees (including both positive and negative angles)

A
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4
Q

State the Cosine Rule

A

The cosine rule is as follows:

a2 = b2 + c2 - 2bc cosA

or

b2 = a2 + c2 - 2bc cosB

or

c2 = a2 + b2 - 2bc cosC

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5
Q

How do you convert degrees to radians?

A

Given that 1º = πc/180

to convert ‘n’ degrees to ‘rad’ multiply ‘n’ as follows:

nº x πc/180º = nπc/180

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6
Q

How do you convert from Radians to Degrees?

A

Given that 1c = 180º/π

to convert ‘n’ radians to degrees multiply ‘n’ as follows:

nc x 180º/πc = 180nº/π

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7
Q

How can you determine the length of an arc using radius length and angle in radians?

A

Given an angle of radians you can use the following formula:

s = rØ

note: the units of the arc length will be the same as those of the radius.

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8
Q

How can you determine the Area of a Sector given a radius and an angle in Radians?

A

Given a radius and and angle in radians the area of a sector can be determined using the following equation:

A = ½r2Ø

note: the units of the area are equal to those of the radius squared.

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9
Q

How can you determine the area of a sector given a radius and an angle in degrees?

A

Given a radius and and angle in degrees the area of a sector can be determined using the following equation:

A = Ø/360 • πr2

note: the units of the area are equal to those of the radius squared.

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10
Q

How can you determine the length of an arc using radius length and an angle in degrees?

A

Given an angle of degrees you can use the following formula:

s = Ø/360 • 2πr

note: the units of the arc length will be the same as those of the radius.

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11
Q

Given a radius and an angle in radians, how can you calculate the area of a segment?

A

Given that the Area of a Sector is ½r2Ø, Ø in radians

and the Area of the Triangle is ½r2 SinØ

The Area of the Segment = ½r2Ø - ½r2 SinØ

= ½r2(Ø - SinØ)

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12
Q

Given a radius and an angle in Degrees, how can you determine the Area of a Segment?

A

Given that the Area of a Sector is Ø/360•πr2, Ø in degrees

and the Area of the Triangle is ½r2 SinØ

The Area of the Segment = Ø/360•πr2 - ½r2 SinØ

= ½r2(Øπ/180 - SinØ)

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13
Q

What are the three basic reciprocal trigonometric identities and there definitions?

A

Sec x = 1/Cos x (The secant function)

Cosec x = 1/Sin x (The cosecant function)

Cot x = 1/Tan x (The cotangent function)

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14
Q

What are the three Triangle Trig Identities and their variations?

Hint: the first is equal to 1, and the others are derived from it.

A

sin2x + cos2x = 1

var1 : 1 - sin2x = cos2x

var2 : 1 - cos2x = sin2x

1 + tan2x = sec2x

var1 : tan2x = sec2x - 1

var2 : 1 = sec2x - tan2x

1 + cot2x = cosec2x

var1 : cot2x = cosec2x - 1

var2 : 1 = cosec2x - cot2x

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15
Q

What are the Sine Compound-Angle Forulae?

A

Sin(x + y) = Sin(x) Cos(y) + Cos(x) Sin(y)

Sin(x - y) = Sin(x) Cos(y) - Cos(x) Sin(y)

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16
Q

What are the Cosine Compound-Angle Formulae?

A

Cos(x + y) = Cos(x) Cos(y) - Sin(x) Sin(y)

Cos(x - y) = Cos(x) Cos(y) + Sin(x) Sin(y)

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17
Q

What are the Tangent Compound-Angle Formulae?

A

Tan(x + y) = [Tan(x) + Tan(y)] / [1 - Tan(x) Tan(y)]

Tan(x - y) = [Tan(x) - Tan(y)] / [1 + Tan(x) Tan(y)]

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18
Q

What are the Double-Angle Formulae?

A

Sin 2x = 2 Sinx Cosx

Cos 2x = Cos2x - Sin2x

= 2 Cos2x - 1

= 1 - 2 Sin2x

Tan 2x = [2 Tanx] / [1 - Tan2x]

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19
Q

What is the ratio of Sin 30º?

A

Sin 30º = ½

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20
Q

What is arcsin (½) in degrees?

A

sin-1 (½) = 30º

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21
Q

What is the ratio of sin π/6?

A

sin π/6 = ½

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22
Q

What is the arcsin (½) in radians?

A

sin-1 (½) = π/6

23
Q

What is the ratio of sin (45º)?

A

sin (45º) = 1/√2

= √2/2

24
Q

What is arcsin (√2/2)?

A

sin-1 (√2/2) = 45º

25
Q

What is the ratio of sin (π/4)?

A

sin (π/4) = 1/√2

= √2/2

26
Q

What is arcsin (√2/2) in radians?

A

sin-1 (√2/2) = π/4

27
Q

What is the ratio of sin (60º)?

A

sin (60º) = √3/2

28
Q

What is arcsin (√3/2) in degrees?

A

sin-1 (√3/2) = 60º

29
Q

What is the ratio of sin (π/3)?

A

sin (π/3) = √3/2

30
Q

What is arcsin (√3/2) in radians?

A

sin-1 (√3/2) = π/3

31
Q

What is the ratio of cos (30º)?

A

cos (30º) = √3/2

32
Q

What is arc-cos (√3/2) in degrees?

A

cos-1 (√3/2) = 30º

33
Q

What is the ratio of cos (π/6)?

A

cos (π/6) = √3/2

34
Q

What is arc-cos (√3/2) in radians?

A

cos-1 (√3/2) = π/6

35
Q

What is the ratio of cos (45º)?

A

cos (45º) = 1/√2

= √2/2

36
Q

What is arc-cos (√2/2) in degrees?

A

cos-1 (√2/2) = 45º

37
Q

What is the ratio of cos (π/4)?

A

cos (π/4) = 1/√2

= √2/2

38
Q

What is arc-cos (√2/2) in radians?

A

cos-1 (√2/2) = π/4

39
Q

What is the ratio of cos (60º)?

A

cos (60º) = ½

40
Q

What is arc-cos (½) in degrees?

A

cos-1 (½) = 60º

41
Q

What is the ratio of cos (π/3)?

A

cos (π/3) = ½

42
Q

What is arc-cos (½) in radians?

A

cos-1 (½) = π/3

43
Q

What is the ratio of tan (30º)?

A

tan (30º) = 1/√3

= √3/3

44
Q

What is arctan (√3/3) in degrees?

A

tan-1 (√3/3) = 30º

45
Q

What is the ratio of tan (π/6)?

A

tan (π/6) = 1/√3

= √3/3

46
Q

What is arctan (√3/3) in radians?

A

tan-1 (√3/3) = π/6

47
Q

What is the ratio of tan (45º)?

A

tan (45º) = 1

48
Q

What is arctan (1) in degrees?

A

tan-1 (1) = 45º

49
Q

What is the ratio of tan (π/4)?

A

tan (π/4) = 1

50
Q

What is arctan (1) in radians?

A

tan-1 (1) = π/4

51
Q

What is the ratio of tan (60º)?

A

tan (60º) = √3

52
Q

What is arctan (√3) in degrees?

A

tan-1 (√3) = 60º

53
Q

What is the ratio of tan (π/3)?

A

tan (π/3) = √3

54
Q

What is arctan (√3) in radians?

A

tan-1 (√3) = π/3

Engineering Maths (3 decks)

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