Step 1: Understand that tan^(-1)(5/12) means we are looking for an angle whose tangent is 5/12.
Step 2: Draw a right triangle where the opposite side is 5 and the adjacent side is 12 (since tangent = opposite/adjacent).
Step 3: Use the Pythagorean theorem to find the hypotenuse. Calculate it as: hypotenuse = sqrt(opposite^2 + adjacent^2) = sqrt(5^2 + 12^2) = sqrt(25 + 144) = sqrt(169) = 13.
Step 4: Now, we can find the cosine of the angle. Cosine is defined as adjacent/hypotenuse.
Step 5: Substitute the values: cos(tan^(-1)(5/12)) = adjacent/hypotenuse = 12/13.
Trigonometric Functions – Understanding the relationship between angles and side lengths in right triangles, particularly how to derive cosine from the tangent function.
Inverse Trigonometric Functions – Using inverse functions to find angles and subsequently applying trigonometric ratios.
Pythagorean Theorem – Applying the Pythagorean theorem to find the hypotenuse when given the lengths of the other two sides.
