Hi guys, we are working with trig ratios.
I’m going to work with one word it is called contrast.
What is contrast means?
It takes 2 opposites and put them in next to each other and contrasting them showing
the differences and you can highlight and dramatize an idea if you want to show how
tall something is you put something short next to it so you get opposite when you put
them together.
Well this 2 opposite here is called sine and cos, well they got different type of angle
system and what we are going to do is show you can have these 2 guys and come up with
the same answer on a ratio so let’s use the example here right next to me.
We have a right angle triangle, there’s a little right angle down there little friend
there it is.
And we’ve got angles around this and we’ve got lengths.
Now the lengths we have is 5 for they hypotenuse, over here we have 3 and over here down the
bottom on this length we have 4.
Now what the question asked here is to find the sine thither as a ratio, so if we are
looking for a sine thither, quite simply what we do write down - sine thither which is going
down here so working with this angle – sine thither equals –now what the sine thither
equal again?
It’s opposite over what?
Opposite over hypotenuse – now if we look at this we will find an opposite it is straight
isn’t it like that?
So it is straight opposite the sine thither pointing right across there is the number
3.
So let’s write them first of all opposite – over a hypotenuse so let’s get back
to that again – opposite is 3 so let’s write down 3 – so it’s 3 over – now
over what?
Hypotenuse here – so it’s hypotenuse – hypotenuse here is 5 so sine thither quite simply is
3/5 yeah so this are 3/5 now what we are looking for is cos 90 minus thither for the second
part of this question let’s look at that now.
Looking for cos bracket 90 minus thither now if you never come across this I’m going
to show you how to understand this strategy involved here.
Cos minus 90 thither is clearly is not in our diagram isn’t it we can’t see it in
the triangle.
We have thither here and we kind in the empty angle up here so I’m going to work it out
up here.
Now what is 90 minus thither exactly?
Well it works like this, you know how all angles set up to a 180 degrees in the triangle,
when we have a thither here no matter how what it may be, if we have thither here and
we have a 90 here whatever is left clearly it has to be 90 minus thither.
Whatever that angle is take away that whatever is left is going to give us that.
So this angle here would be 90 minus thither, let me just put that in – we have 90 minus
thither – now that’s the angle in there because angle some of the triangles are explained.
So if that’s90 minus thither we are looking for cos 90 minus thither I wonder what that’s
going to equal.
So first of all what does cos equals – cos equals adjacent isn’t it, what is adjacent
is to the angle so we are looking for angle we got adjacent 3 again – so let’s write
down the adjacent– adjacent over what?
Cos is adjacent over hypotenuse – over hypotenuse let us see what is that equal.
Adjacent for cos 90 minus thither so that is a cos now so we are going down, the adjacent
is to the left there right so it’s 3 – so that is equal 3 over hypotenuse – over 5
so it’s clearly what we have here is 2 contrast cos sine and both come up with exactly the
same answer.
Sine thither is 3/5 and cos 90 minus thither is also 3/5.
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