00:01
Hello students, here it is given that cos theta equal to minus 8 by 9 where theta is in the second quadrant.
00:21
We know that in second quadrant sine and cosine functions are only positive and the remaining all functions will be negative.
00:52
So here from cos theta we can write it as cos theta equal to adjacent side by hypotenuse side.
01:00
Here let us make the triangle to represent the data that is here by comparing with the given cos theta.
01:20
Adjacent side is 8, therefore bc equal to 8 and hypotenuse is 9, therefore ac equal to 9.
01:27
Here let us consider the opposite side be x.
01:32
First we can find x to find second theta and third theta.
01:36
Therefore by the progress theorem ac square equal to ab square plus bc square.
01:56
Here ac is 9, therefore 9 square equal to ab is 8, therefore x square plus 8 square.
02:05
Hence x square equal to 9 square minus 8 square that is 81 minus 64.
02:11
Then x equal to square root of 17.
02:18
Here we can say that x is root of 17...