Question

Find the exact value of cot 7pi/4 & sec13pi/6 including quadrant location

Answer 1

First we will convert those radian angles to degrees, since my mind works better with degrees.  Let's work one at a time.  First, $\frac{7 \pi }{4} * \frac{180}{ \pi }=315$.  If we start at the positive x-axis and measure out 315 we end up in the 4th quadrant with a reference angle of 45 with the positive x-axis.  The side across from the reference angle is -1, the side adjacent to the angle is 1, and the hypotenuse is sqrt2.  The cotangent of this angle, then is 1/-1 which is -1.  As for the second one, converting radians to degrees gives us that $\frac{13 \pi }{6} * \frac{180}{ \pi } =390$.  Sweeping out that angle has us going around the origin more than once and ending up in the first quadrant with a reference angle of 30° with the positive x-axis.  The side across from the angle is 1, the side adjacent to the angle is √3, and the hypotenuse is 2.  Therefore, the secant  of that angle is 2/√3.