Trigonometry and Wave Function

Question 1

π radians =

Answer 1

180 degrees

Question 2

30 degrees in radians

Answer 2

π/6 radians

Question 3

45 degrees in radians

Answer 3

π/4 radians

Question 4

60 degrees in radians

Answer 4

π/3 radians

Question 5

90 degrees in radians

Answer 5

π/2 radians

Question 6

135 degrees in radians

Answer 6

3π/4 radians

Question 7

360 degrees in radians

Answer 7

2π radians

Question 8

how to convert from degrees to radians

Answer 8

multiply by π and divide by 180

Question 9

how to convert from radians to degrees

Answer 9

multiply by 180 and divide by π

Question 10

describe exact values triangle for 45 degrees

Answer 10

right angled triangle

45 degrees at each of other vertices

root 2 on hypotenuse

1 on other sides

Question 11

describe exact values triangle for 30/60 degrees

Answer 11

right angled triangle

1 along base
2 on hypotenuse
root 3 on other side

60 in angle between 1 and 2
30 in angle between 2 and root 3

Question 12

how to work out exact values for 0,90,180,360 etc.

Answer 12

trig graphs

Question 13

when would there be no solutions for sin/cos

Answer 13

has to be greater than or equal to -1 and less than or equal to 1

Question 14

what does sin2x mean?

Answer 14

there are 2 cycles of sin graph in 360 degrees

Question 15

what part of the question should you pay close attention to when deciding how many answers are required?

Answer 15

the domain

Question 16

if there is a squared term what should you remember

Answer 16

that it could be positive or negative when you square root so will need to work out solutions in all quadrants

Question 17

what should be noted if an angle is acute?

Answer 17

a cast diagram is not necessary

Question 18

what is the result when we add or subtract angles?

Answer 18

a compound angle

Question 19

sin (A+B) =

Answer 19

sinAcosB + cosAsinB

Question 20

sin (A-B) =

Answer 20

sinAcosB - cosAsinB

Question 21

cos (A+B) =

Answer 21

cosAcosB - sinAsinB

Question 22

cos (A-B) =

Answer 22

cosAcosB + sinAsinB

Question 23

how to layout question asking you to prove one of the compound angle formulas using given numbers

Answer 23

work out LHS and RHS separately then state “since LHS=RHS, the claim it true for…”

Question 24

how to find the exact value of sin75

Answer 24

sin(45+30)

Question 25

if a question gives you values for sin p and sin q, how do you calculate sin(p+q)?

Answer 25

1. draw triangles out (sin=o/h)
2. use pythagoras to work out other side and therefore the values of cos p and cos q
3. use compound angle formula

Question 26

sinx / cosx =

Answer 26

tan x

Question 27

sin squared x + cos squared x =

Answer 27

1

Question 28

1 - cos squared x =

Answer 28

sin squared x

Question 29

1 - sin squared x =

Answer 29

cos squared x

Question 30

double angle formula for sin2A

Answer 30

2sinAcosA

Question 31

double angle formula for cos2A

Answer 31

cos squared A - sin squared A
2cos squared A - 1
1 - 2sin squared A

Question 32

further trig equations: how to use double angle formula to solve trig equations

Answer 32

1. replace 2A term using double angle formula
2. make sure every term is on one side and equation is equal to zero
3. factorise the expression and then solve each part

Question 33

wave function: how to work out k

Answer 33

square root of p squared + q squared

Question 34

wave function: how to work out tan a

Answer 34

ksina / kcosa

Question 35

simple wave function question steps

Answer 35

1. expand kcos(x-a) using compound angle formula
2. rearrange so you can compare with pcosx + qsinx
3. state values of ksina and kcosa
4. CAST diagram
5. find k and a
6. state pcosx + qsinx in the form kcos(x-a) using these values

Question 36

steps for wave function with multiple angles

Answer 36

exactly the same as before but use kcos(2x-a) or whatever number/form in question

Question 37

what are the maximum and minimum values of the sine and cosine functions?

Answer 37

maximum 1

minimum -1

Question 38

how to work out maximum value of a trigonometric function

Answer 38

1. follow wave functions steps
2. max value of k occurs when kcos(x-a)=k
3. rearrange to find x

Question 39

how to solve equation that involves both a sin(nx) and a cos(nx) term

Answer 39

1. wave function steps as normal
2. equal kcos(x-a) to RHS
3. rearrange and use CAST diagram to solve for x (answers in suitable quadrants and double check the domain)

Question 40

how to sketch the graph of y=pcosx+qsinx

Answer 40

1. write in form kcos(x-a)

2. k is amplitude and a is the phase shift (check if there is also a shift up/down)