Question

What is the exact value of sec(-405degress)??

Answer 1

sec= 1/(cos), you can add or subtract 360 degrees from any angle measurement without changing the value of any of the trig functions i.e. 405 degrees= 405-360=45. cos of 45 is \[\sqrt{2}/2\] so sec405= 2/sqrroot2

Answer 2

it is \[\frac{1}{\cos (-405)}\]
Since cosine is an even function \[\cos(-405) = \cos(405)\]
Also 405 - 360 = 45 so
\[\cos (405)=\cos (45)=\frac{\sqrt{2}}{2}\]
so\[\frac{1}{\cos(-405)} = \frac{1}{\cos(45)} = \frac{1}{\frac{\sqrt{2}}{2}}=\frac{2}{\sqrt{2}}=\sqrt{2}\]