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Mathematics > Trigonometry > Flashcards

Trigonometry Flashcards

0
Q

Sine rule to find an angle

A

SinA over a is equal to SinB over b

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1
Q

Sine Rule to find a side

A

a over sinA is equal to b over sinB

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2
Q

Cosine rule to find a side

one buddy buddy

A

a squared = b squared plus c squared minus two bc cosA

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3
Q

Complementary angles

A 
Sin♎️= cos(90-♎️) and visa versa
Tan♎️= cot(90-♎️) and visa versa
Cosec♎️= sec(90-♎️) and visa versa
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4
Q

Types of trigonometric equations

A

1) single angle
2) multiple angle
3) square angle
4) compound angles

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5
Q

Single angles

A

Solve for ♎️ within a given domain.

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6
Q

Multiple angle

A

When solving a multiple angle you must

1) multiply the domain by the coefficient of ♎️ and therefore introduce a new pronumeral
e. g. Sin2♎️=1/2 for 0 sinx=1/2 for 0<720
2) solve for the new pronumeral e.g. x
3) substitute the unknown term back in for x and solve

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7
Q

Square angle

A

When solving a square angle you must move the square outside the brackets and root the other side. You will end up with a plus minus, ie both positive and negative angles in all fourvquadrants

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8
Q

Compound angle

A

In a compound angle a term inside brackets will see ♎️ added, subtracted, multiplied, divided by numbers. Much like double angles, whatever is happening to ♎️ must happen to the domain when the bracketed term is let to be x or a pronumeral.

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9
Q

Trig graphs sinx and cosecx

A

Sinx- walks up the mountain and down the valley

Cosecx- suction cups

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10
Q

Trig graphs cosx and secx

A

Cosx- gets cut short at 1/2 a mountain ‘late bloomer’

Secx- 1/2 suction cups

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11
Q

Trig graphs tanx and cotx

A

Tanx- 3 strip vertical flag

Cotx- rebel goes opposite way

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12
Q

Trig identity 1

A

Tan♎️=Sin♎️/cos♎️

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13
Q

Trig identity 2

A

Cot♎️=Cos♎️/sin♎️

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14
Q

Trig identity 3

A

Sin squared ♎️ + cos squared ♎️ = 1

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15
Q

Trig identity 4

A

1 + cot squared ♎️= cosec squared ♎️

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16
Q

Trig identity 5

A

Tan squared ♎️ + 1= sec squared ♎️

17
Q

Sin sum of angles

A

Sin(x+y)= sinx cosy + cosx siny

18
Q

Sin difference of angles

A

Sin(x-y)= sinx cosy- cosx siny

19
Q

Cos sum of angles

A

Cos(x+y)= cosx cosy - sinx siny

20
Q

Cos difference of angles

A

Cos(x-y)= cosx cosy+ sinx siny

21
Q

Tan sum of angles

A

Tan(x+y)= tanx + tany/ 1- tanx tany

22
Q

Tan difference of angles

A

Tan(x-y)= tanx- tany/ 1+ tanx tany

23
Q

Sin ratio of double angles

A

Sin2x= 2 sinx cosx

24
Q

Cos ratio of double angles

A

Cos2x = cos squared x - sin squared x
= 1-2sin squared x
= 2 cos squared x - 1

25
Q

Tan ratio of double angles

A

Tan 2x= 2tanx/ 1- tan squared x

26
Q

Sin♎️ ratio in terms of tan♎️/2

A

Sin♎️= 2t/ 1+ t squared

Sin favourite so + bottom

27
Q

Cos♎️ ratio in terms of tan♎️/2

A

Cos♎️= 1-t squared/ 1+ t squared
MISH MASH MIDDLE
but bottom still positive

28
Q

Tan♎️ ratio in terms of tan♎️/2

A

Tan♎️= 2t/ 1-t squared

Tan is a weird minus bottom

29
Q

Solving Further Trigonometric Equations

A

asin♎️ +/- bcos♎️ OR acos♎️ +/- bsin♎️

30
Q

Sin further trig equations

A

1) asin♎️+bcos♎️= rsin(♎️+♉️)

2) asin♎️-bcos♎️= rsin(♎️-♉️)

31
Q

Cos further trig equations

A

1) acos♎️+ bsin♎️= rcos(♎️-♉️)

2) acos♎️- bsin♎️= rcos(♎️+♉️)

32
Q

Further trig equations r=

A

r= root a squared plus b squared

33
Q

Further trig equations ♉️

A

Tan♉️= b/a

34
Q

Solving further trig equations

A

1) convert the equation into asin or acos form
2) using this form find a and b and hence r and ♉️
3) convert to r sin/cos(♎️+♉️) form and use compound angles to solve

35
Q

Sin general solution

A

If sin♎️=sin♉️, then

♎️=180n + ♉️(-1)^n

36
Q

Cos general solution

A

If cos♎️=cos♉️, then

♎️=360n +/- ♉️

37
Q

Tan general solution

A

If tan♎️=tan♉️, then

♎️=180n+♉️

38
Q

Radians to degrees

A

multiply radians by 180/pi

39
Q

Degrees to radians

A

Multiply degrees by pi/180

Mathematics (12 decks)

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