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irina [24]
3 years ago
13

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

Mathematics
1 answer:
Gennadij [26K]3 years ago
3 0
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.
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