What are the sin, tan, cos rules eg +180?

What are the sin, tan, cos rules eg +180?

I am thinking of those As level/ add maths questions that need you to remember those rules

They are all mixed up everywhere in my notes I would apprciate it if you could show me

Eg sin is X
X
X
X
Cos is

Then show me what Sin is when it's negative eg

I am afraid I don't have a clue of what you are on about. You will need to elaborate a bit more.

What are the sin, tan, cos rules eg +180?

I am thinking of those As level/ add maths questions that need you to remember those rules

They are all mixed up everywhere in my notes I would apprciate it if you could show me

Eg sin is X
X
X
X
Cos is

Then show me what Sin is when it's negative eg
x
x
x

etc

For example you need to know the rules for sin in this question Part ii

no problem For example you need to know the rules for sin in this question Part ii

I think you mean these:

$\displaystyle sinx = sin(x\pm 360) [br]\displaystyle cosx=cos(x\pm 360)[br]\displaystyle cosx=cos(-x)[br]\displaystyle sinx=sin(180-x)[br]\displaystyle tanx=tan(x\pm 180)[br]$

Yes this Can you give me a quick example for each of them or a few if you have time?
So I can get it into my head

Thank you!

I think you mean these:

$\displaystyle sinx = sin(x\pm 360) [br]\displaystyle cosx=cos(x\pm 360)[br]\displaystyle cosx=cos(-x)[br]\displaystyle sinx=sin(180-x)[br]\displaystyle tanx=tan(x\pm 180)[br]$

Cos = 360 - x
Sin = 180 - x
Tan = 180 + x

Do you need to know about the reciprocated trig ratios?

Yes this Can you give me a quick example for each of them or a few if you have time?
So I can get it into my head

Thank you!

You said + and -



You only said + not +and -

Who is right? An example would really help here THanks

Yes this Can you give me a quick example for each of them or a few if you have time?
So I can get it into my head

Thank you!

I think you mean these:

$\displaystyle sinx = sin(x\pm 360) [br]\displaystyle cosx=cos(x\pm 360)[br]\displaystyle cosx=cos(-x)[br]\displaystyle sinx=sin(180-x)[br]\displaystyle tanx=tan(x\pm 180)[br]$

e.g.

$\displaystyle sin30 =0.5[br]sin(30+360)=sin390=0.5[br]sin(30-360)=sin(-330)= 0.5[br][br]cos60=0.5[br]cos(-60)=0.5[br]$

You can check all of these on your calculator and you will see these all work.

So if you have to find all the solutions of, $\displaystyle sinx=0.4$ in the interval between 0 and 360 then you will do this,
$\displaystyle x=sin^{-1}(0.4)=23.57817848$
$\displaystyle sin(180-x)=0.4 \implies 180-x=sin^{-1}(0.4)=23.57817848 \implies x=180-23.5=156^o$

Ok thanks I will learn them The quadrent seems really long and hard to understand.

I already learn CAST today and these rules will make it easier.

you need to visualise the four different quadrants on a graph. Any blank graph will do.



Sin is positive in the 1st And 2nd quadrant.

Cos is positive in the 1st and 4th quadrant.

Tan is positive in the 1st and 3rd quadrant.

So now, looking at a question.

Work out the two values of x . sin(1/2)=x

work out sin^-1(1/2) on your calc and you will find out it is 30 degrees.

That is only one value, you need to find the other value for x.

now looking back to what i said earlier, sin is positive in the 1st and 2nd quadrant. We need to find the value of x in the 2nd quadrant.

How do we do this?

Answer, we simply do 180 - 30 = 150

because 30 is the first value. Basically we're looking for a mirror image if you look at the quadrant picture i included.

Let me know if you don't understand, i can give you another example to try.

I know you use the quadratics to get (2 sin x -1)(sin x +3)= 0

But how did they get there?? I never used quadratics with sinx in it .... I have only done it with numbers.


Moving on
Can you show me the degree marks on the quadrent? I know it's 30 degrees in the first quad, no problem

I know sin is also in second quadrent (I know using CAST)

But why do you do 180 - 30?
Why not 180 + 30?