trigonometry

Question 1

how to solve this question

Answer 1

Question 2

how to solve this question

Answer 2

Question 3

how to solve this question

Answer 3

Question 4

to find the other solutions when solving a trig function for sin

Answer 4

180 - x

Question 5

to find other solutions when solving a trig function for cos

Answer 5

360 - x and 360 + x

Question 6

to find other solutions when solving a trig function for tan

Answer 6

180 + x

Question 7

how to solve this question

Answer 7

Question 8

how to solve this question

Answer 8

steps:
1) hidden quadratic so sub sin = y
2) solve for y and factorise
3) replace y with sin again and solve for x

Question 9

what is a trig identity linkig sin and cos = 1

Answer 9

Question 10

what is a trig identity linking sin and cos to tan

Answer 10

Question 11

Answer 11

Question 12

Answer 12

Question 13

Answer 13

Question 14

sin and cosec graph

Answer 14

Question 15

cos and sec graph

Answer 15

Question 16

tan and cot graph

Answer 16

Question 17

what are 2 Pythagorean identities

Answer 17

Question 18

cot and cosec pythagoream identity

Answer 18

1 with a cot is cosy

Question 19

tan and sec pythagoream identity

Answer 19

1 with a tan is secsy

Question 20

prove that

Answer 20

Question 21

what has to happen for us to have inverse functions (draw it on a graph)

Answer 21

1-to-1 mapping

Question 22

how to do the domain and range of arcsin

Answer 22

steps:
1) must have 1-to-1 mapping so restrict domain of sin to pie/2 and -pie/2
2) range would be -1 and 1 for sin
3) for arc sin switch the domain and range around

Question 23

how to do the domain and range of arccos

Answer 23

steps:
1) must have 1-to-1 mapping restrict domain of cos to 0 and pie
2) the range would be 1 and -1
3) for arccos switch the domain and range around

Question 24

how to do the domain and range of arctan

Answer 24

steps:
1)must have 1-to-1 mapping so restrict the domain to pie/2 and -pie/2
2) the range won’t exist as it is an asymptote and won’t intercept the y values
3) for arctan switch the domain and range so the domain would be XER

Question 25

what are the 3 trignometric identities

Answer 25

Question 26

manipulating trig identities

Answer 26

Question 27

manipulating trig identities (3 ways to write the cos double angle formula

Answer 27

Question 28

manipulating trig identities

Answer 28

Question 29

how to do this question

Answer 29

steps: 1) use the sin double angle formula 2) calculate the trig with B in it as they are an actual answer and not x 3) solve for x

Question 30

how to do a harmonic form question (R-method)

Answer 30

steps: 1) use the double angle formula on the RHS 2) set the LHS cos = RHS cos and same for sin 3) find R using Pythagoras 4) divide the sin function by the cos one 5) you get tan and solve for alpha PART B 1) use the RHS answer of the last question 2) solve like a normal trig question

Question 31

what is the minimum for this (harmonic form)

Answer 31

Question 32

what is the minimum value for this harmonic form

Answer 32

denominator needs to be the biggest to make the smallest value (minimum)

Question 33

how to solve a and b of this harmonic form question

Answer 33

steps: 1) sin double angle formula on the RHS 2) set the 5 to sin and 12 to cos 3) find R 4) put 5/12 = tanx 5) solve for x PART B 1) work out the max which is the biggest possible value 13+7 2) the minimum would be -13 + 7 which is -6

Question 34

what is one key rule for using small angle approximations

Answer 34

Question 35

small angle approximation for sin

Answer 35

Question 36

small angle approximation for cos

Answer 36

Question 37

small angle approximation for tan

Answer 37

Question 38

small approximation question

Answer 38

steps: 1) use the small approximations for cos and tan 2) expand 3) need to know if x is small (in order to use approximation) x^3 is tiny therefore = 0

Question 39

Answer 39

Question 40

Answer 40

Question 41

Answer 41

Question 42

Answer 42

Question 43

Answer 43

Question 44

Answer 44

Question 45

how to differentiate sin by first principles

Answer 45

https://youtu.be/1fsvZBy0m3Q?si=80vadC-T8dr7NK84