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

See the image below,

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?

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.

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

Wait hang on, first part?

do you mean part i?

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

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?

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.

You can just replace sin x like that?!
$\displaystyle y=sinx$

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, $\displaystyle (2x-1)(x+3)=0 \implies (2sinx-1)(sinx+3)=0$

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

I think you mean these:
$\displaystyle sinx = sin(x\pm 360) [br]\displaystyle cosx=cos(x\pm 360)[br]\displaystyle cosx=cos(-x)[br]\displaystyle sinx=sin(180-x)[br]\displaystyle tanx=tan(x\pm 180)[br]$

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