1. ## Half/Double angle Problem

Given that $\sin u=\frac{7}{25}$ and $\tan u<0$
Find the exact value of $\cos u,
\sin 2u,
\cos 2u,
\tan 2u,
$

I was absent this day in class and am not sure about where to start with this problem. I obviously know that you won't do them all, and I don't expect you to or else I'd never learn! But guidance on how to do find $\cos u$ and possibly one of the double angle ones would be greatly appreciated.

2. $\sin(a+b) = \sin(a)\cos(b) + \cos(a)\sin(b)$
$\cos(a+b) = \cos(a)\cos(b) - \sin(a)\sin(b)$

You can derive the double angle identities from these, use $\sin(2u) = \sin(u+u)$.

Also, to find $\cos(u)$ to use in the formulas use the facts $\sin^2(u) + \cos^2(u) = 1$ and $\frac{\sin(u)}{\cos(u)} = \tan(u)$ to determine the sign.

3. Could you clarify how to do the double angle ones please? As for the cos u i got $\displaystyle{\frac{24}{25}}$this was by recognizing that sin is opposite/hypotenuse and then i put the numbers in a triangle and found the adjacent side using Pythagorean theorem and found the side to be 24 and cos is adjacent/hypotenuse so that's how i got that part.

4. First, cosine could be positive or negative. Use the information for tangent to figure out its sign.

Can you try to write the formula for the double angle from the information I have given you before? There should be enough information.