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

1 Answer
Lovecraft
Sep 17, 2015

sec(-227pi/4) = -sqrt2

Explanation:

First let's work that value within the secant to reveal the biggest integer amount of pis, 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)
![http://etc.usf.edu](https://useruploads.socratic.org/b5BFOHRgSAaaEl380uJm_unit-circle7_43215_lg.gif)

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

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