Question

If θ is an angle in standard position and its terminal side passes through the point (-4,-9), find the exact value of \tan\thetatanθ in simplest radical form.

Answer 1

Given:

θ is an angle in standard position and its terminal side passes through the point (-4,-9).

To find:

The exact value of tanθ in simplest radical form.

Solution:

If θ is an angle in standard position and its terminal side passes through the point (x,y), then the exact value of tanθ is:

$\tan \theta=\dfrac{y}{x}$

It is given that, θ is an angle in standard position and its terminal side passes through the point (-4,-9). So, t he exact value of tanθ is:

$\tan \theta=\dfrac{-9}{-4}$

$\tan \theta=\dfrac{9}{4}$

Therefore, the required value is $\tan \theta=\dfrac{9}{4}$.