Question

If tan x = x/y, where x and y are whole numbers, then sin x is:

(a) \(\frac y{\sqrt{y^2 - x^2}}\)

(b) \(\frac x{\sqrt{x^2 + y^2}}\)

(c) \(\frac y{\sqrt{x^2 + y^2}}\)

(d) \(\frac x{\sqrt{y^2 - x^2}}\)

Answer 1

Correct option is (b) \(\frac x{\sqrt{x^2 + y^2}}\)

\(\tan x = \frac xy\)

\(\tan x =\frac PB= \frac xy\)

Here, P is the perpendicular and B is the base.

We know, square of hypotenuse H² = P² + B²

H² = x² + y²

H = \(\sqrt{x^2 + y^2}\)

Hence, sin x = \(\frac PH = \frac x{\sqrt{x^2 + y^2}}\)