How do you evaluate $sec ((-pi)/3)$ ?

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Answer 1 · 2016-11-22T15:55:51

$sec(-pi/3) = 2$

When drawn in standard position, negative angles are clockwise while positive angles are counterclockwise.

Hence, $2pi - |"negative angle"| = "positive angle"$ . Our positive angle is therefore

$2pi - pi/3 = (5pi)/3$

The question becomes evaluate $sec((5pi)/3)$ . We know that $sectheta = 1/costheta$ .

$=> 1/cos((5pi)/3)$

$(5pi)/3$ has a reference angle of $pi/3$ . $cos(pi/3) = 1/2$ , and cosine is positive in quadrant IV.

$=> 1/(1/2)$

$=> 2$

Hopefully this helps!

How do you evaluate sec ((-pi)/3)sec ((-pi)/3)?