I'm doing homework for my trig class, and it's asking for us to use Pythagorean identities to solve for other trig values. I got through the first 10 fine, but I'm stuck on the last three. My teacher has specified that we have to use the pythagorean trig identities... aka:
- $\sin^2 \theta + \cos^2 \theta = 1$
- $1 + \tan^2 \theta = \sec^2\theta$
- $\cot^2 \theta + \ 1 = \csc^2 \theta$
The questions are:
- Given that $x$ is in the first quadrant and $\csc x=1$, what is $\sin x$?
- Given that $x$ is in the first quadrant and $\sec x=\sqrt{2}$, what is $\cos x$?
- Given that $x$ is in the first quadrant and $\sin x=\frac{1}{2}$, what is $\csc x$?
I have no idea where to start using the Pythagorean Identities. Help?