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Original post by blueray

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? ---- Its because 30 degrees is positive so therefore sin is positive so you use 180 - x

Original post by raheem94

Oh yeah I remember now And the same would apply with Tan and Cos (those 2 lines) if it was say 270 degrees?

Can you help answer the quadratic part of the question?

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?

because 180 + 30 is not in the second quadrant. It will be in the third quadrant, hence that would not be the right step.

As i said previously, with sin, your two positive values must be in the first and second quadrant.

Original post by James A

because 180 + 30 is not in the second quadrant. It will be in the third quadrant, hence that would not be the right step.

As i said previously, with sin, your two positive values must be in the first and second quadrant.

Oh yeah this is because CAST involves POSITIVE values! !!!!!! Thanks

All these questions are linking in and making sense!

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

Can you help me on the first part though?

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

Original post by blueray

Oh yeah this is because CAST involves POSITIVE values! !!!!!! Thanks

All these questions are linking in and making sense!

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

Can you help me on the first part though?

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

All these questions are linking in and making sense!

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

Can you help me on the first part though?

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

Wait hang on, first part?

do you mean part i?

Right the reason why its sin 180 - x is because the 30 degrees that you worked out is positive not negative and on your CAST diagram you have S, A, T, C going clockwise. Because the 30 is positive A and S are also + so you substitute 30 in x in both S and A as C and T will be negative. Hope that helps. So it becomes x = 180 - 30 and x = 30

Original post by dugdugdug

Helps if you've seen a graph of these circular functions plotted.

Circular as opposed to hyperbolic, something you'll learn later in conic sections.

Sin is an odd function, ie sin -x=-sin x

Cos is an even function, cos(x)=cos(-x), it's symmetrical about the y-axis

Tan is also odd

Circular as opposed to hyperbolic, something you'll learn later in conic sections.

Sin is an odd function, ie sin -x=-sin x

Cos is an even function, cos(x)=cos(-x), it's symmetrical about the y-axis

Tan is also odd

Does that mean they are both symetrical around the y axis?

Because if thats the case so is sin

Look at this

Original post by James A

Wait hang on, first part?

do you mean part i?

do you mean part i?

No I mean what steps did you use to work out sinx = 1/2

Original post by blueray

No I mean what steps did you use to work out sinx = 1/2

that was just a general example. nothing to do with the real question

Original post by blueray

Oh yeah I remember now And the same would apply with Tan and Cos (those 2 lines) if it was say 270 degrees?

Can you help answer the quadratic part of the question?

Can you help answer the quadratic part of the question?

Your quadratic is, $\displaystyle 2sin^2x+5sinx-3=0$

Let $\displaystyle y=sinx$

So the equation can be written as,

$\displaystyle 2y^2+5y-3=0$

Now factorise the quadratic.

Original post by raheem94

Your quadratic is, $\displaystyle 2sin^2x+5sinx-3=0$

Let $\displaystyle y=sinx$

So the equation can be written as,

$\displaystyle 2y^2+5y-3=0$

Now factorise the quadratic.

Let $\displaystyle y=sinx$

So the equation can be written as,

$\displaystyle 2y^2+5y-3=0$

Now factorise the quadratic.

You can just replace sin x like that?!

$\displaystyle y=sinx$

I thought that wasn't allowed???

Original post by blueray

You can just replace sin x like that?!

$\displaystyle y=sinx$

I thought that wasn't allowed???

$\displaystyle y=sinx$

I thought that wasn't allowed???

It is allowed but at the at the end you will again write it as sinx.

Solving the quadratic will give you, $\displaystyle (2x-1)(x+3)=0 \implies (2sinx-1)(sinx+3)=0$

Original post by raheem94

It is allowed but at the at the end you will again write it as sinx.

Solving the quadratic will give you, $\displaystyle (2x-1)(x+3)=0 \implies (2sinx-1)(sinx+3)=0$

Solving the quadratic will give you, $\displaystyle (2x-1)(x+3)=0 \implies (2sinx-1)(sinx+3)=0$

Thanks

Original post by blueray

Does that mean they are both symetrical around the y axis?

Because if thats the case so is sin

Look at this

Because if thats the case so is sin

Look at this

No, I mean get a graphical calculator (or excel) and plot sin x, cos x and tan x to see what they look like.

It's commonly known as sinusoidal (obviously), a wave like pattern.

Go to google and type in sine graph.

(edited 12 years ago)

Original post by dugdugdug

No, I mean get a graphical calculator (or excel) and plot sin x, cos x and tan x to see what they look like.

It's commonly known as sinusoidal (obviously), a wave like pattern.

Go to google and type in sine graph.

It's commonly known as sinusoidal (obviously), a wave like pattern.

Go to google and type in sine graph.

Below are the graphs, if anyone wants to see them.

Original post by raheem94

I think you mean these:

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

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

Hey, I’ve started maths and further maths this year can you explain to me what does this indicate and when they are used?

Original post by Aesriva

Hey, I’ve started maths and further maths this year can you explain to me what does this indicate and when they are used?

For your information, this is a 12 year old thread, so try to make a new post instead of bumping this. I'm also a Y12 studying maths and further maths I think the author of that post is listing some of the trig 'rules.' My knowledge on A-Level trig is limited but I'll try to explain. Basically, sine and cosine repeat every 360 degrees and tangent repeats every 180 degrees, cos (-x) = cosx (reflecting cosine in the y axis gives the same result), sinx = sin (-x±180) (reflecting sin where the x co-ordinate is ±180 gives the same result). There's nothing more it than that I think.

Also, I'm pretty sure [ br ] is line break in case that confused you.

(edited 2 weeks ago)

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