How this calculator works
Secant takes the reciprocal of cosine. Since cosine lies between minus one and one, a finite secant can never lie strictly between minus one and one. Positive and negative branches touch y=1 and y=-1 at cosine’s extrema and become unbounded near cosine’s zeros. The graph is even and has no finite amplitude. Ratio mode uses arcsec x=arccos(1/x), on 0° to 180° with 90° excluded.
Formula
sec θ=1/cos θ=hypotenuse/adjacent; sec(-θ)=sec θ; sec(θ+2π)=sec θ. A real secant value has |sec θ|≥1.
Worked example
sec 60°=1/(1/2)=2. sec 180°=-1. A secant value of -2 returns the principal angle 120°.
Advertisement
Frequently asked questions
Is secant the same as inverse cosine?
No. Secant is the reciprocal 1/cos θ. Inverse cosine, or arccos, takes a ratio and returns an angle.
Can secant equal zero?
No. The reciprocal of a finite cosine cannot be zero.
Why is secant undefined at 90°?
Cosine is zero there, and dividing one by zero is undefined.