Core 3 - Trigonometry Flashcards
What is the trig identity with cot^2x
1 + Cot ^2 X = cosec^2 X
What is the trig identity involving tan^2x
1 + tan^2 X = sec^2 X
What is the trig identity that equates to cot X
Cos X/sin X = cot X
What are the three trigonometry identities that equate inverse functions?
Cot X = 1/tan X
Sec X = 1/cos X
Cosec X = 1/sin X
What is the domain and range of tan(-1) (x)
Domain: x belongs to the reals
Range: -(pi)/2
What is the rule for finding the end points of an inverse trig graph?
Swap x and y co-ordinates around, as the graph has been reflected in y=x
What are the end points of cos-1(x)
Top left point = (-1)(pi)
Bottom right point = (1,0). This was the starting point on the y axis for cos(x)
What are the end points for sin-1(x)
Bottom left = (-1, -pi/2)
Top right = (1, pi/2)
Why do we limit the domain of inverse trig graphs?
So that they are one to one functions. We can then find the inverse
What is the domain we use for sin(x) when finding the inverse?
-pi/2 –> pi/2 inclusive. THis gives us our two maximum points
What is the domain used for the inverse of cos(x)
0-pi inclusive.
What does the domain of the starting function become when we plot the inverse?
The range. Like any inverse function, domain and range have been swapped as it is reflected in y=x
Where are the assymptotes on tan-1(x)
y=+-(pi/2)
What is the domain and range of cot(x)
d: x =/= n(pi)
r: cot(x) belongs to reals
What is the domain and range of sec(x)
d: x=/= pi/2 + n(pi)
r: sec(x)>1,
What is the domain and range of cosec(x)
d: x=/= n(pi)
r: cosec(x)>1,
When transforming an equation in x, what are the steps?
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.
When stating the range of tan-1(x), what must you be careful of?
The range goes up to the assymptotes, but does not equal them, so (pi/2)
When drawing a graph of tan-1(X), what must you remember?
There are assymptotes at +-(pi/2) so you can’t label end points
If given limits for a modulus graph when solving an inequality, what must you remember?
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.
When solving cos^2(x) =2, how must you rearrange?
cos(x)=+-(2)^0.5
DO NOT MISS -VE SOLNS
What is 12sec^2(x) written as in terms of cos^2(x)
12/cos^2(x), DEFINITELY NOT
1/12cos^2(x)
What can you look to do if your trig proof involves (1+-sinx)
Multiply top/bottom by the conjugate i.e. (1-+sinx), to give you DOTS, which can be rewritten as cos^2(x)
What can you do if you have a quadratic expression in cos(x)?
factorise it and look to cancel.
When solving trig functions like cos(2x+30)=0.5, how do you make sure you don’t miss solutions?
Modify the given range for x for 2x+30, and make sure PV+360 is outside range, or you have an extra value.
What are the end points for sin-1(3x)
(1/3, pi/2)
-1/3, -pi/2
What are the end points for 3cos-1(x)
(-1, 3pi)
1,0
How do you find the domain of a trig equation like tan(2x+73) for 0
Follow BIDMAS to find the new domain
02+73
1802+73
73
When using trig identity to solve trig equation, what you do you?
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
How do you solve a trig equation where cos^2(x)=2?
Solve cos(x)=+-(1/2). YOU WILL MISS SOLUTIONS IF YOU DON’T INCLUDE THE NEGATIVE!!!
