Question

Find the value of tan θ for the angle shown. A line is drawn from the origin through the point square root of thirty-three comma negative four. The angle theta is given as the measurement from the positive x axis counterclockwise to the line.

Answer 1

If you draw this triangle on a graph as described, tan theta is -4(square root)33/33

Answer 2

Answer:

The value of tan θ is:

             $\tan \theta=-\dfrac{4}{\sqrt{33}}$

Step-by-step explanation:

From the given right angled triangle we have:

          Base of the triangle i.e. OA is: √33 units

and Perpendicular length of triangle  i.e. AB is: 4 units

Hence, in the given right angled triangle we will use the trignometric ratio corresponding to the angle (360°-θ) as:

$\tan (360-\theta)=\dfrac{perpendicular}{base}\\\\\\\tan (360-\theta)=\dfrac{4}{\sqrt{33}}$

As we know that:

$\tan (360-\theta)=-\tan \theta$

Hence,

$-\tan \theta=\dfrac{4}{\sqrt{33}}\\\\\\i.e.\\\\\\\tan \theta=-\dfrac{4}{\sqrt{33}}$

                     Hence, the answer is:

               $\tan \theta=-\dfrac{4}{\sqrt{33}}$