Trigonometry

Question 0

Sine rule to find an angle

Answer 0

SinA over a is equal to SinB over b

Question 1

Sine Rule to find a side

Answer 1

a over sinA is equal to b over sinB

Question 2

Cosine rule to find a side

one buddy buddy

Answer 2

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

Question 3

Complementary angles

Answer 3

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

Question 4

Types of trigonometric equations

Answer 4

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

Question 5

Single angles

Answer 5

Solve for ♎️ within a given domain.

Question 6

Multiple angle

Answer 6

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

Question 7

Square angle

Answer 7

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

Question 8

Compound angle

Answer 8

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.

Question 9

Trig graphs sinx and cosecx

Answer 9

Sinx- walks up the mountain and down the valley

Cosecx- suction cups

Question 10

Trig graphs cosx and secx

Answer 10

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

Secx- 1/2 suction cups

Question 11

Trig graphs tanx and cotx

Answer 11

Tanx- 3 strip vertical flag

Cotx- rebel goes opposite way

Question 12

Trig identity 1

Answer 12

Tan♎️=Sin♎️/cos♎️

Question 13

Trig identity 2

Answer 13

Cot♎️=Cos♎️/sin♎️

Question 14

Trig identity 3

Answer 14

Sin squared ♎️ + cos squared ♎️ = 1

Question 15

Trig identity 4

Answer 15

1 + cot squared ♎️= cosec squared ♎️

Question 16

Trig identity 5

Answer 16

Tan squared ♎️ + 1= sec squared ♎️

Question 17

Sin sum of angles

Answer 17

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

Question 18

Sin difference of angles

Answer 18

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

Question 19

Cos sum of angles

Answer 19

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

Question 20

Cos difference of angles

Answer 20

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

Question 21

Tan sum of angles

Answer 21

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

Question 22

Tan difference of angles

Answer 22

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

Question 23

Sin ratio of double angles

Answer 23

Sin2x= 2 sinx cosx

Question 24

Cos ratio of double angles

Answer 24

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

Question 25

Tan ratio of double angles

Answer 25

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

Question 26

Sin♎️ ratio in terms of tan♎️/2

Answer 26

Sin♎️= 2t/ 1+ t squared | Sin favourite so + bottom

Question 27

Cos♎️ ratio in terms of tan♎️/2

Answer 27

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

Question 28

Tan♎️ ratio in terms of tan♎️/2

Answer 28

Tan♎️= 2t/ 1-t squared | Tan is a weird minus bottom

Question 29

Solving Further Trigonometric Equations

Answer 29

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

Question 30

Sin further trig equations

Answer 30

1) asin♎️+bcos♎️= rsin(♎️+♉️) | 2) asin♎️-bcos♎️= rsin(♎️-♉️)

Question 31

Cos further trig equations

Answer 31

1) acos♎️+ bsin♎️= rcos(♎️-♉️) | 2) acos♎️- bsin♎️= rcos(♎️+♉️)

Question 32

Further trig equations r=

Answer 32

r= root a squared plus b squared

Question 33

Further trig equations ♉️

Answer 33

Tan♉️= b/a

Question 34

Solving further trig equations

Answer 34

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

Question 35

Sin general solution

Answer 35

If sin♎️=sin♉️, then | ♎️=180n + ♉️(-1)^n

Question 36

Cos general solution

Answer 36

If cos♎️=cos♉️, then | ♎️=360n +/- ♉️

Question 37

Tan general solution

Answer 37

If tan♎️=tan♉️, then | ♎️=180n+♉️

Question 38

Radians to degrees

Answer 38

multiply radians by 180/pi

Question 39

Degrees to radians

Answer 39

Multiply degrees by pi/180