Trigonometry in computer science
Rotations: that arise in Computer Graphics and Robotics , through rotation matrices, Quaternions, etc.
 Cordics  for computing these functions on a Microprocessor / FPGA
 Transforms in Image Compression and elsewhere  , e.g. FFT computation in $O(n \log n)$ time
Anything to do with the interface between CS and Signal Processing 
Pretty much anywhere in navigation and tracking, e.g. anything involving a GPS, IMU,etc.
Somewhat indirectly in  Computational Geometry (CG), in its application like in coverage &amp; localization in wireless sensor networks.


.. to name a few! So if you want to really avoid trig functions, you should  learn CG :-)