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

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

(edited 12 years ago)

Scroll to see replies

Original post by blueray

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 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.

Original post by GreenLantern1

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

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

Original post by blueray

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

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

I think you mean these:

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

Original post by blueray

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

Cos = 360 - x

Sin = 180 - x

Tan = 180 + x

Original post by raheem94

I think you mean these:

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

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

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!

Original post by blueray

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!

So I can get it into my head

Thank you!

Also

Sin(-x)= Sinx

Cos(-x)=Cosx

Original post by raheem94

I think you mean these:

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

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

You said + and -

Original post by TLK

Cos = 360 - x

Sin = 180 - x

Tan = 180 + x

Sin = 180 - x

Tan = 180 + x

You only said + not +and -

Who is right? An example would really help here THanks

Do you need to know about the reciprocated trig ratios?

You should be able to work them out yourself just by thinking about the graphs!

e.g: cos(x+90) = sin(-x) ?

e.g: cos(x+90) = sin(-x) ?

(edited 12 years ago)

Original post by GreenLantern1

Do you need to know about the reciprocated trig ratios?

Do we need to know that for add maths?

Original post by blueray

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!

So I can get it into my head

Thank you!

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,

$\displaystyle x=sin^{-1}(0.4)=23.57817848$

$\displaystyle sin(180-x)=0.4 \implies 180-x=sin^{-1}(0.4)=23.57817848 \implies x=180-23.5=156^o$

Original post by blueray

You said + and -

You only said + not +and -

Who is right? An example would really help here THanks

You only said + not +and -

Who is right? An example would really help here THanks

Just learn all the expressions i have written.

However, i like to use a quadrant diagram rather then using this method.

Original post by blueray

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!

So I can get it into my head

Thank you!

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.

Original post by raheem94

I think you mean these:

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

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

Original post by raheem94

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,

$\displaystyle x=sin^{-1}(0.4)=23.57817848$

$\displaystyle sin(180-x)=0.4 \implies 180-x=sin^{-1}(0.4)=23.57817848 \implies x=180-23.5=156^o$

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

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.

Original post by blueray

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.

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

Is there a difference between the cast and quadrant diagram?

I think they are both the same.

Original post by James A

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.

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?

(edited 12 years ago)

Lol we were taught in school to remember sex and the city i.e Sin 180 - x (sex), All = x (and), Tan 180 + x (the), Cos 360 - x (city).

Original post by blueray

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?

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?

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