When we plot the angle given to be 17pi/6, we will find out that it is equal to one revolution and 150 degrees. Therefore, it is found in the second quadrant of a cartesian plane and that its coterminal angle is 30 degrees. Since it is in the second quadrant, the value of its cosine should be the negative of the cosine of its coterminal angle. The cosine is -0.866. Then, we find its reciprocal in order to solve for the secant. The final answer would be -1.15.