High students, welcome to this section where we deal with trigonometry.
Now let's get started understanding some of the basic terminology in trigonometry.
Over here, I have a right angle triangle ABC.
Right.
You can see this angle over here is a 90 degree angle.
Now, let's take that this angle.
It is theta degrees.
All right.
Now, then I can see that side.
EBR is the Eddison side for Angle Theta, right.
It's the side that is at the center data.
And you can't take the hypotenuse as the adjacent side.
Right in this triangle is the hypotenuse and Abey's is one more side.
So these two sides are next to detA.
Now the adjacent side is the side that is next to Peter and is not the hypotenuse.
All right.
Now you can see that side.
ABC is the opposite side or angle Teater.
So Abe is the adjacent side and Beezy is called the opposite side.
And remember, Acey is the hypotenuse.
That is it's the side that is opposite the 90 degree angle.
All right.
Now, we have learned these two important terminologies that we use in trigonometry.
Now let's get into S.T. de Costa and a.T.M.
First, we will understand what we mean with this, and then we will learn some interesting things about
this.
All right.
Let's get started over here again.
I have my triangle, ABC and this angle over here is the study group.
Now, let's take an example.
Let the sides of this triangle be three, four and five centimeter.
All right.
Now, let's start with sine data.
Sine Deda is defined as the opposite side, divided by the hypotenuse.
Now, over here we have pizza right now.
Let's find S.T. for this angle.
So that would be the ratio between four, right?
Because four is the opposite side.
Right.
This is the side opposite the double and the hypotenuse.
The hypotenuse is easy.
That's five units over here.
So done in this case is four divided by five.
Now, if this angle over here is Alpha, let's find sine Alpha.
Also sign Alpha is opposite side by hypotenuse.
The side opposite alpha is equal to three centimetre.
Right.
This is the opposite side.
Right.
So that's three.
And you divide it by the hypotenuse, that's easy, which is equal to five centimeter, so sine alpha
over here is equal to three by five.
All right.
We have seen that SINTA is equal to opposite side by hypotenuse.
All right.
Now let's proceed and find what we mean with cost theta.
All right.
Gosta is defined as the ratio between the adjacent side and the hypotenuse.
So in this case, over here you have Titta.
So which is the adjacent side to angle to that side Ebright.
Therefore Kosti will be equal to three.
That's the adjacent side divided by the hypotenuse which is Acey, and that's equal to five because
it is equal to three by five.
Now let's find course Alpha also to the adjacent side to Alpha is B.C. right is the side next to Alpha.
Other than the hypotenuse.
So we have B.C. over here, right?
That's the adjacent side.
And the hypotenuse is E, C, that's five.
So cos Alpha is equal to four by five.
All right.
So we have seen sine data and.
Now let's see the third important ratio that Santita and tanty is defined as the opposite side, divided
by the adjacent side.
Now over here you have titta.
The opposite side is four, right.
So in this ratio the numerator is equal to four and the adjacent side would be three.
Right.
So you have three over here.
So Tante is equal to four by three.
Now can you tell me what would be an Alpha and alpha would be three by four.
Right.
Because three is the opposite side and four is the adjacent.
Now, an interesting thing to note over here is that data can also be obtained by taking the ratio of
sine detA and Kerstetter.
Now, what is Santita S.D. four divided by five.
Right.
So let's write that and Kosti days three by five.
Right adjacent by opposite.
So three by five.
Now when you take the ratio of four by five, divided by three by five, this five and this five gets
canceled and you are left with four by three.
So tanty is also equal to sign.
detA by Kosti to.