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# why is sec(-3pi) equal to -1 and not 0?

how do you solve without just relying on the unit circle.

### 2 Answers

- Anonymous8 years agoFavorite Answer
sec(-3π) = 1/cos(-3π) --> that you should just know. sec(x) = 1/cos(x)

cos(-3π) = -1

1/-1 = -1

The negative really doesn't matter. 3π means that is went around the unit circle one and a half times. so 3π and -3π are equivalent here

- oldprofLv 78 years ago
sec(theta) = 1/cos(theta) where theta is an interior angle to a right triangle.

theta = -3pi radians = pi radians so that cos(pi) = -1 and sec(-3pi) = sec(pi) = 1/cos(pi) = 1/(-1) = -1

That's why. The deal is in recognizing that - 3pi radians == pi radians. If you don't see this, I suggest you lay the angles out on a polar coordinate system where theta = 0 is on the X axis to the right, theta = pi/2 is on the Y axis straight up, etc. Remember, the minus sign, as in -3pi, turns the angles in the opposite direction, CS rather than CCW which is the normal direction of increasing angles.