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Section 1.3 : Trig Functions
6. Determine the exact value of sec(−11π6) without using a calculator.
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Hint : Even though a unit circle only tells us information about sine and cosine it is still useful for secant so sketch a unit circle and relate the angle to one of the standard angles in the first quadrant.
First, we can notice that π6−2π=−11π6 and so (remembering that negative angles are rotated clockwise) we can see that the terminal line for −11π6 will form an angle of π6 with the positive x-axis in the first quadrant. In other words, −11π6 and π6 represent the same angle. So, we’ll have the following unit circle for this problem.
Hint : Given the obvious symmetry here use the definition of secant in terms of cosine to write down the solution.
Because the two angles −11π6 and π6 have the same coordinates the answer is,
sec(−11π6)=1cos(−11π6)=1√3/2=2√3