00:01
Here on this problem, we've been told that the cosine of theta is equal to one -third.
00:04
And when we want to use identities to find other trick functions here, starting with the sign of theta.
00:10
Now, the sign of theta is equal to the square root of one minus the cosine squared of theta.
00:17
So since the cosine is one -third, this tells us that this is equal to one minus one -third squared, which is equal to the square root of one minus one over nine, which is equal to the square root of eight over nine, which is 2 root 2 over 3.
00:44
And so the sine of theta is equal to 2 root 2 over 3.
00:52
Now in part b, we're looking for the tangent of theta.
00:59
Now the tangent of theta, as we know, is equal to the sine of theta over the cosine of theta.
01:07
The sine of theta is 1 3.
01:10
I'm sorry, the sine of theta is 2 root 2 over 3, and the cosine of theta is 1 3...