00:01
In this question, we have to remind the value of sine to theta, cost to theta, and tan to theta.
00:05
We're 2 theta because where theta lies is in quadrant 4 and tan theta is given over here.
00:14
Okay, so if tan theta is given and theta is in quadrant 4, then it becomes pretty much easy for us to find the other two, as in sign and cost.
00:22
Because if this is theta, then tan is opposite which is 5 over adjacent which is 12.
00:27
And hypotenous, let's say, is h.
00:28
So as per the pythagoras theorem, h square is 5 square plus 12 square, which means that h square is 25 plus 144, which is 169.
00:38
So taking square root both sides, h is 13.
00:42
So now we can easily write the value of sine and cosine, because that will be required in finding all this.
00:49
So sign is opposite, which is 5 over hypotenuse, which is h, which is 13.
00:54
But mind it in quadrant 4, sign is negative.
00:56
So we've got to place a minus sign over here.
00:59
Likewise, cosine will be adjacent, which is 12 over hypotenous, which is 13.
01:03
But in quadrant 4, cost is positive.
01:06
So, cost will remain positive.
01:08
Now, let's find everything one by one.
01:11
What is sine 2 theta? sign 2 theta is 2, sine theta, cost theta.
01:16
So, sine theta, we already found as negative 5 over 13.
01:20
Cosine is 12 over 13...