00:01
Okay, we are told here that sine theta is negative 1213th and the angle theta lies in the fourth quadrant, which means cosine is plus but sign is minus.
00:11
And tan, of course, would be minus.
00:15
Now, the technique here is to draw a triangle like this, put theta here, and sine is 12, 13, not drawn to scale, obviously.
00:28
And the missing side will be five.
00:32
It's a 5, 12, 13 triangle.
00:35
So, first question says, find the value of sine 2 theta.
00:43
Well, sine 2 theta is twice sine theta cos theta, the standard formula.
00:50
Sign theta is negative 12 over 13.
00:55
And cosine theta is plus in the fourth quadrant, so it's 5 over 13.
01:01
So we get here negative overall 120 over 169.
01:10
That's the first one.
01:15
Now, cosine 2 theta is cosquared theta minus sine squared theta or 1 minus 2 sine squared theta...