Core 3 - Trigonometry

Question 1

What is the trig identity with cot^2x

Answer 1

1 + Cot ^2 X = cosec^2 X

Question 2

What is the trig identity involving tan^2x

Answer 2

1 + tan^2 X = sec^2 X

Question 3

What is the trig identity that equates to cot X

Answer 3

Cos X/sin X = cot X

Question 4

What are the three trigonometry identities that equate inverse functions?

Answer 4

Cot X = 1/tan X
Sec X = 1/cos X
Cosec X = 1/sin X

Question 5

What is the domain and range of tan(-1) (x)

Answer 5

Domain: x belongs to the reals
Range: -(pi)/2

Question 6

What is the rule for finding the end points of an inverse trig graph?

Answer 6

Swap x and y co-ordinates around, as the graph has been reflected in y=x

Question 7

What are the end points of cos-1(x)

Answer 7

Top left point = (-1)(pi)

Bottom right point = (1,0). This was the starting point on the y axis for cos(x)

Question 8

What are the end points for sin-1(x)

Answer 8

Bottom left = (-1, -pi/2)

Top right = (1, pi/2)

Question 9

Why do we limit the domain of inverse trig graphs?

Answer 9

So that they are one to one functions. We can then find the inverse

Question 10

What is the domain we use for sin(x) when finding the inverse?

Answer 10

-pi/2 –> pi/2 inclusive. THis gives us our two maximum points

Question 11

What is the domain used for the inverse of cos(x)

Answer 11

0-pi inclusive.

Question 12

What does the domain of the starting function become when we plot the inverse?

Answer 12

The range. Like any inverse function, domain and range have been swapped as it is reflected in y=x

Question 13

Where are the assymptotes on tan-1(x)

Answer 13

y=+-(pi/2)

Question 14

What is the domain and range of cot(x)

Answer 14

d: x =/= n(pi)
r: cot(x) belongs to reals

Question 15

What is the domain and range of sec(x)

Answer 15

d: x=/= pi/2 + n(pi)
r: sec(x)>1,

Question 16

What is the domain and range of cosec(x)

Answer 16

d: x=/= n(pi)
r: cosec(x)>1,

Question 17

When transforming an equation in x, what are the steps?

Answer 17

1) what is x or y being replaced by?
2) Are the transformations affecting the same axis?
3) If yes, do opposite of bidmas (translations first). If no, do please carry on in which every order you like.

Question 18

When stating the range of tan-1(x), what must you be careful of?

Answer 18

The range goes up to the assymptotes, but does not equal them, so (pi/2)

Question 19

When drawing a graph of tan-1(X), what must you remember?

Answer 19

There are assymptotes at +-(pi/2) so you can’t label end points

Question 20

If given limits for a modulus graph when solving an inequality, what must you remember?

Answer 20

If there is a bottom limit, there is an inequality between the minimum and the point at which the two lines intersect, for example y=e^-1 + e and y=4.

Question 21

When solving cos^2(x) =2, how must you rearrange?

Answer 21

cos(x)=+-(2)^0.5

DO NOT MISS -VE SOLNS

Question 22

What is 12sec^2(x) written as in terms of cos^2(x)

Answer 22

12/cos^2(x), DEFINITELY NOT

1/12cos^2(x)

Question 23

What can you look to do if your trig proof involves (1+-sinx)

Answer 23

Multiply top/bottom by the conjugate i.e. (1-+sinx), to give you DOTS, which can be rewritten as cos^2(x)

Question 24

What can you do if you have a quadratic expression in cos(x)?

Answer 24

factorise it and look to cancel.

Question 25

When solving trig functions like cos(2x+30)=0.5, how do you make sure you don’t miss solutions?

Answer 25

Modify the given range for x for 2x+30, and make sure PV+360 is outside range, or you have an extra value.

Question 26

What are the end points for sin-1(3x)

Answer 26

(1/3, pi/2)

-1/3, -pi/2

Question 27

What are the end points for 3cos-1(x)

Answer 27

(-1, 3pi)

1,0

Question 28

How do you find the domain of a trig equation like tan(2x+73) for 0

Answer 28

Follow BIDMAS to find the new domain
02+73
1802+73
73

Question 29

When using trig identity to solve trig equation, what you do you?

Answer 29

Rearrange trig equation to look as much like one side of the identity as possible, then equate it to the other side of the identity

4tanθ- tan^2 θ=1
4tanθ=1+tan^2 θ
2tanθ/(1 + tan^2θ)=
sin⁡(2θ)=1/2

Question 30

How do you solve a trig equation where cos^2(x)=2?

Answer 30

Solve cos(x)=+-(1/2). YOU WILL MISS SOLUTIONS IF YOU DON’T INCLUDE THE NEGATIVE!!!