Solve, $\cos(x)=\frac 25, \frac{3\pi}{2}A. Draw and label two triangles, one containing angles $x$ and one
containing angle $y$. (can use the $x-y$ axis version of triangles)
B. List $\sin(x), \cos(x), \sin(y)$, and $\cos(y)$
c. Find $\sin(x+y)$
d. Find $\sin(2x)$
e. Find $\cos(\frac y2)$
 A: HINT:
To obtain $\cos(y)$ and $\sin(x)$ use the basic trigonometric inequality:
$$\sin^2x + \cos^2x = 1$$
But note that $x$ is in the fourth quadrant, while $y$ is in the second. What does that say about the sign?
For the three calculation they are just basic trigonometric identities. You can find a load of them here and also you can find the identities you need.
HINT 2:
For problem A. Use the fact that cosine is an even function. Because $x$ is in the fourth quadrant we can write $x = 360^{\circ} - \alpha$, where $\alpha$ is an obtuse angle so we have:
$$\cos (x) = \cos(360^{\circ} - \alpha) = \cos (- \alpha) = \cos {\alpha}$$
Now since $\cos (x) = \frac{adjacent}{hypothenuse}$, we can easy draw a right triangle with side 2 and hypothenuse 5. From this you obtain $\alpha$ and subsequently $x$.
Note that $x > \pi$, so a triangle with angle $x$ would be impossible to construct, because the sum of the interior angles in a triangle is $\pi$.
For sine use the fact that $\sin (\pi - \alpha) = \sin {\alpha}$ and $sin x = \frac{opposite}{hypothenuse}$
