## anonymous 5 years ago What is the exact value of sec(-405degress)??

1. anonymous

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

2. anonymous

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$\frac{1}{\cos(-405)} = \frac{1}{\cos(45)} = \frac{1}{\frac{\sqrt{2}}{2}}=\frac{2}{\sqrt{2}}=\sqrt{2}$