Question

Find the formula for this function.

A. y = tan
B. y = cotx
C. y = tanx
D. y = secx

Answer 1

Check the picture below, now that's a template for transformations, however let's notice, that tangent has and cotangent have a period of π, we know is not secant, because secant usually goes parabolic up and down, this one looks more like tangent or cotangent, but from the picture above, it has a period of 2π, that is, from 0 to 2π it begins repeating, let's use that template below to find the value for "B".

`2\pi =\cfrac{\pi }{B}\implies B=\cfrac{\pi }{2\pi }\implies B=\cfrac{1}{2} \\\\[-0.35em] ~\dotfill\\\\ f(x)=\stackrel{A}{1}\tan(\stackrel{B}{(1)/(2)}x+\stackrel{C}{0})+\stackrel{D}{0}\implies f(x)=\tan((1)/(2)x)\implies f(x)=\tan((x)/(2))`

Answer 2

The correct formula for the function based on a right triangle in trigonometry, involving the ratio of the opposite to the adjacent side, is C. y = tanx.

Step-by-step explanation:

The question is asking to find the formula for a function based on trigonometric concepts. When considering a right triangle as described in the provided information, the tangent function (tan) is the ratio of the side opposite to angle A (Ay) to the side adjacent to angle A (Ax). Therefore, if the formula involves the ratio of the opposite to the adjacent side of a right triangle, the correct answer would be C. y = tanx.

To solve for the components or the magnitude and direction of a vector in trigonometry, it is often necessary to use the tangent function. For instance, if we are given a problem where 0 = tan-1 (Ay/Ax), this indicates that we are working with the angle whose tangent is Ay/Ax, which relates to the definition of the tangent function.