Students in this video, let's start analyzing two important triangles, this will help us retain the
important sine cos andante values already over here have Triangle ABC and the angles of triangle ABC
are forty five degrees, 45 degrees and 90 degrees.
Now in Triangle Park you are the anchors are 60 degrees, thirty degrees and 90 degrees.
So we have marked the angles over here.
Now let's see Triangle ABC.
You can see that these two angles are equal to we haven't isosceles right triangle over here.
So therefore if this is of X units, this side also will be of X units and hence AC will be of root
of X squared plus X squared units.
Right.
That's equal route root 2x.
Therefore the ratio of sites of abs to is to AC will be of the form.
One is two, one is to root two.
All right.
But we need to remember this, this will help us a lot.
Now let's see triangle P.
Q are the ratio of sides of triangle P.
Q Are will be in the form root three over here, one over here and two over here.
All right.
Now what are the things that we can note the side opposite the bigger angle will be bigger.
Right over here you have root three and over here you have one through Rotary's opposite sixty degrees.
So it's the bigger value and one is opposite thirty degrees.
Now the value of Rotary's around one point seven.
Right.
So it's greater than one hundred and ninety degrees.
The biggest angle.
So you have two opposite ninety degrees.
All right.
Now we can see that this is a right angle triangle.
Right.
Therefore over here, if you square this, you have one square and if you square root three, you have
three.
Right.
The one plus three gives you four.
And when you take root of four.
Right, you get that equal to two.
And that's the two over here.
So it's following the Pythagoras Theorem property.
All right.
Now, if we remember these two triangles, that is if you remember the ratio of the sides in the case
of these two triangles, we can easily remember a lot of the important sine cos and tan ratios.
All right.
So let's keep this aside.
OK, now let's get on with the important sign costs and then values, and you need to remember this,
and this is a memory aid for you to remember these values.
Now, let's start filling this table.
What would be signed 30.
Now you have a 30 degree angle over here, right?
The sign is opposite by hypotenuse.
So that would be one divided by two.
Right.
So sign 30 is equal to one by two.
And we write that over here.
What about cost 30?
Now, again, we have the 30 degree angle over here causes a descent by hypotenuse.
That's Route three, divided by two.
Right.
Similarly, what is done down is opposite by Addison.
That would be one by route.
So let's write these values.
We have cost 30 as Route three by two and then 30 as one by Route three.
All right.
Now let's get to 45 five.
What is St. Peter?
Its opposite by hypotenuse.
So if this is forty five, sine forty five is one by route.
Right, let's right that over here.
What would be cost.
Forty five.
It's a by hypotenuse that's also equal to one by two.
And what is ten.
Forty five.
It's opposite by Addison.
That's one by one.
And you get it as one.
So let's write these values over here.
Cost forty five is one by two and then forty five is equal to one.
All right.
Now what about sixty degrees.
What is sine sixty.
You have a 60 degree angle over here.
Sine is opposite by adjacent, opposite by hypotenuse.
So that would be route three by two.
Right.
We are Route three by two over here.
Similarly 60 will be one by two.
Right.
That's adjacent by hypotenuse.
We have one by two over here.
And what would be ten.
Sixty, that's route three divided by one.
That's equal to Route three right now.
Let's go to the zero degree angle.
Now, imagine you have a triangle over here and the sides are X, Y, and this side is each.
And this angle over here is data.
Now, you can imagine that when Tita becomes zero, right, this value of X becomes zero.
Right.
As you keep reducing T to the value of X will keep producing.
And when two is equal to zero, X will be equal to zero.
Right now what is s.A.
That's X by X, right?
90 days equal to in that triangle, 70 days X by H.
Now if X is equal to zero, this becomes zero.
That's why you signed zero is equal to zero.
All right.
Now what about cost zero.
Let's think it in this manner.
In this case, when detail is zero, right.
It becomes equal to white.
That is why it becomes equal to X.
These two values are equal.
Right.
And what is costing over here?
Because that is why you buy it.
And because these are equal, you get cost.
It is equal to one.
Right.
All right.
Now let's proceed to Dante de de de de de de divided by Costeja.
That's zero divided by one, and that is equal to zero.
Right?
So we have got the values of sine cos and tan data when data is equal to zero.
All right, let's proceed.
Now what about the case?
Twenty two is equal to ninety degree.
When Peter is equal to ninety degrees, this X will become equal to its right.
You can think of it in this manner.
As you keep increasing data rate, the value of X will keep increasing and it is approaching the value
of X, right.
So when data is equal to 90 degree X will be equal to X.
Right.
Therefore S.E De which is X by x rayed, that would be one because these two values are equal.
So sine 90 is equal to one.
What about cost ninety at this case, where to is ninety, you can see that Y will be equal to zero.
Right.
You can think of it in this manner as this keeps increasing, this keeps decreasing.
But when X is equal to its right is just one straight line over here.
That is why is equal to zero now cost is equal to Y by each so that would be zero by eight which is
equal to zero to cost.
Ninety is equal to zero and and data is equal to sign because that's one divided by zero.
Right.
And that is equal to infinity or it is not defined because division by zero is not defined.
Let me write that again.
Division by zero is not defined now or here.
We have got the important properties and with this you will be able to solve any trigonometry question.