How large can tan θ be? Briefly explain and justify your reasoning.

Answer 1

tangent of an angle approaches infinity as the angle approaches 90 degrees or 90+360n for n= any integer

tangent of an angle = opposite side over adjacent side

as the angle approaches 90 degrees the opposite side approaches 1, and the adjacent side approaches 0. Any fraction with 0 as the denominator is undefined or = infinity. The tangent approaches an infinitely large number, with no limit to how large.

try a few examples: tan88 = about 29, tan89 = about 57

tan89.9 = 573, tan89.99 = about 5730, tan89.999 = about 57300.

it keeps increasing without limit,