Final answer:
A trigonometric formula that has sec(x) is sec(x) = 1/cos(x) and the Pythagorean identity sec^2(x) = 1 + tan^2(x). Secant is the reciprocal of cosine and is used in various applications such as vector resolution and calculating components of forces in physics.
Step-by-step explanation:
A trigonometric formula that includes sec(x) is the identity sec(x) = 1/cos(x). The function 'sec' stands for secant, which is the reciprocal of the cosine function. For example, if we have a right triangle with sides x (adjacent), y (opposite), and h (hypotenuse), and let x/h be the cosine of angle θ, then the secant of θ is simply h/x. Another useful identity involving secant is the Pythagorean identity sec2(x) = 1 + tan2(x), where 'tan' stands for the tangent of angle θ, which is y/x for a right triangle.
In problems involving vectors or conservation of momentum, understanding how to manipulate and use these trigonometric functions can be crucial. For instance, if the direction and magnitude of a vector are known, one can resolve the vector into its scalar components along the x and y axes using cos(x) and sin(x) respectively.