Step 1: Understand that tan^(-1)(3/4) means we have a right triangle where the opposite side is 3 and the adjacent side is 4.
Step 2: Use the Pythagorean theorem to find the hypotenuse of the triangle. The hypotenuse (h) can be calculated as h = sqrt(opposite^2 + adjacent^2) = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5.
Step 3: Now, we need to find cos(tan^(-1)(3/4)). In a right triangle, cosine is defined as the adjacent side divided by the hypotenuse. Here, the adjacent side is 4 and the hypotenuse is 5.
Trigonometric Identities – Understanding the relationship between trigonometric functions and their inverses, particularly how to derive cosine from the tangent function.
Right Triangle Relationships – Using the properties of right triangles to find the lengths of sides based on given ratios, such as those derived from the tangent function.
