What are the sine, cosine, and tangent of 7 pi over 4 radians?

Look at the graph below.  The red triangle is in the fourth quadrant, where sin is negative, cos is positive and tan is negative.  With this in mind we can see that

$$\\ \sin(\frac{7\pi}{4})=-\sin(\frac{\pi}{4})=-\frac{1}{\sqrt2}\\ \cos(\frac{7\pi}{4})=\cos(\frac{\pi}{4})=\frac{1}{\sqrt2}\\ \tan(\frac{7\pi}{4})=-\tan(\frac{\pi}{4})=-1$$