Using the unit circle, how do you find the value of the trigonometric function: sec(-227pi/4) ?

1 Answer
Sep 17, 2015

#sec(-227pi/4) = -sqrt2#

Explanation:

First let's work that value within the secant to reveal the biggest integer amount of #pi#s, so we can eliminate them by looking at the period:
#sec(-227pi/4) = sec(-56pi -3pi/4)#

The period of the secant is #2pi# so
#sec(-56pi -3pi/4) = sec(-28(2pi)-3pi/4) = sec(-3pi/4)#

The secant is an even function, that is, #f(-x) = f(x)#
So, #sec(-3pi/4) = sec(3pi/4)#

Now, we can either just look at the unit circle or continue using formulas. Since you specifically asked for the unit circle, we should look for #cos(3pi/4)#
etc.usf.edu

We see that #cos(3pi/4) = -sqrt2/2# or #cos(3pi/4) = -1/sqrt2#
So, #sec(3pi/4) = 1/cos(3pi/4) = -sqrt2#