Formula to find the Angle between two slopes I have given two slopes $m_1 = \frac{1}{2}$ and $m_2 = 1$
While finding the angle I made use of the formula $\tan(\theta) = \frac{m_1-m_2}{1+m_1m_2}$
answer is : $\theta = \arctan(\frac{-1}{3})$
But in book the answer is $\theta = \arctan(\frac{1}{3})$.
what would be the right answer?
 A: $$
\frac{1-\frac12}{1+1\cdot\frac 12} = \frac 1 3, \qquad \frac{\frac12-1}{1+\frac12\cdot1} =-\frac13.
$$
Either of these is the angle between those two lines.  Where two lines intersect they form angles with measures adding up to $180^\circ$.  If $\alpha+\beta=180^\circ$ then $\tan\alpha = - \tan\beta$.
A: Correct formula with sign convention positive for  $\theta$ counter-clockwise rotation from direction of radius vector $1$ to $2$ is  
$$\tan(\theta) = \dfrac{m_2-m_1}{1+m_1m_2}.$$
A: You might not observed the modules in the formula. They remove the negative signs. So the answer you get | -1/3 | becomes +1/3. So the answer in the book is correct. 
A: The solution given in the book is correct. The actual formula says, one needs to take the absolute value of (m1-m2)/(1+m1.m2), before you perform a tan inverse (arctan), in order to evaluate the final value of angle between two line segments.
Magnitude OR Absolute value OR Modulus of any number is always positive (it is without regard to it's sign, negative or positive). So, it ALWAYS will be arctan of some positive number.
