Question

If `sin θ = a/b`, then tan θ is equal to ______.

Options

• `a/sqrt(b^2 - a^2)`

• `b/sqrt(b^2 - a^2)`

• `sqrt(b^2 - a^2)/a`

• `sqrt(b^2 - a^2)/b`

Answer 1

If `sin θ = a/b`, then tan θ is equal to `underlinebb(a/sqrt(b^2 - a^2))`.

Explanation:

From `sin θ = a/b`, think of a right triangle with opposite = a and hypotenuse = b.

By Pythagoras the adjacent side = `sqrt(b^2 - a^2)`.

Then `tan θ = "Opposite"/"Adjacent"`

= `a/sqrt(b^2 - a^2)`

Assumes b² > a², so the square root is real; sign depends on the quadrant.