Final answer:
To rewrite sec in terms of its cofunction, use the relationship between sec and csc, and the cofunction identity, resulting in sec(θ) = 1/sin(90° - θ). You can tackle reciprocals and cofunctions by applying neutralizing operations, such as rooting a squared value.
Step-by-step explanation:
To rewrite sec in terms of its cofunction, you must understand the relationship between trigonometric functions and their cofunctions. The secant (sec) is the reciprocal of the cosine (cos), and it has a cofunction relationship with the cosecant (csc), which is the reciprocal of the sine (sin). In a right triangle, the cosecant of an angle is the hypotenuse divided by the opposite side, while the secant is the hypotenuse divided by the adjacent side. Due to this relationship, sec(θ) can also be written in terms of sin using the identity sec(θ) = 1/cos(θ) = 1/sin(90° - θ), because sin and cos are cofunctions, meaning sin(θ) = cos(90° - θ).
When dealing with reciprocals and cofunctions, to 'invert' a mathematical function such as squaring, you can raise it to the power that will neutralize the original operation, like square rooting to find the side length of a right triangle when you have a squared value from the Pythagorean Theorem.