I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 1.3 : Trig Functions
6. Determine the exact value of \(\displaystyle \sec \left( { - \frac{{11\pi }}{6}} \right)\) without using a calculator.
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First, we can notice that \(\frac{\pi }{6} - 2\pi = - \frac{{11\pi }}{6}\) and so (remembering that negative angles are rotated clockwise) we can see that the terminal line for \( - \frac{{11\pi }}{6}\) will form an angle of \(\frac{\pi }{6}\) with the positive \(x\)-axis in the first quadrant. In other words, \( - \frac{{11\pi }}{6}\) and \(\frac{\pi }{6}\) represent the same angle. So, we’ll have the following unit circle for this problem.
Because the two angles \( - \frac{{11\pi }}{6}\) and \(\frac{\pi }{6}\) have the same coordinates the answer is,
\[\sec \left( -\frac{11\pi }{6} \right)=\frac{1}{\cos \left( -\frac{11\pi }{6} \right)}=\frac{1}{{}^{\sqrt{3}}/{}_{2}}=\frac{2}{\sqrt{3}}\]