Secant Definition

The secant of an angle is defined as the reciprocal of its cosine, so it tells you the "flip" of the cosine value. This works because cosine gives the adjacent-to-hypotenuse ratio in a right triangle, and taking the reciprocal turns that into hypotenuse-to-adjacent. In any context where cosine is nonzero, secant is just another way to express the same angle information.

Use secant when a problem gives you cosine and asks for the reciprocal, or when an expression is written in terms of secants rather than cosines. It also appears in trigonometric identities, calculus, and some geometry problems involving right triangles and periodic functions.

• Using secθ as cosθ instead of 1/cosθ
• Forgetting that secant is undefined when cosθ = 0
• Leaving the reciprocal un-simplified or not rationalizing the denominator when required