Tan x is defined as which ratio?

Tan x is defined as which ratio?

• A. sin x / cos x
• B. cos x / sin x
• C. sin x * cos x
• D. 1 / cos x

Answer: (A)

Tan x is defined as the ratio of the sine to the cosine: tan x = sin x / cos x, with the restriction that cos x ≠ 0. This comes from thinking in a right triangle: tan is opposite over adjacent, and using sin and cos definitions (sin x = opposite/hypotenuse, cos x = adjacent/hypotenuse), you get tan x = (opposite/hypotenuse) / (adjacent/hypotenuse) = opposite/adjacent. On the unit circle, tan x also equals y/x, which is sin x / cos x. The other expressions correspond to cot x (cos x / sin x), the product sin x cos x, and sec x (1 / cos x), none of which define tan x.

Tan x is defined as the ratio of the sine to the cosine: tan x = sin x / cos x, with the restriction that cos x ≠ 0. This comes from thinking in a right triangle: tan is opposite over adjacent, and using sin and cos definitions (sin x = opposite/hypotenuse, cos x = adjacent/hypotenuse), you get tan x = (opposite/hypotenuse) / (adjacent/hypotenuse) = opposite/adjacent. On the unit circle, tan x also equals y/x, which is sin x / cos x. The other expressions correspond to cot x (cos x / sin x), the product sin x cos x, and sec x (1 / cos x), none of which define tan x.