Find angle between two lines by given equations

Question

I have equations: $3x + y - 2 = 0$ and $4x - 2y + 5 = 0$. My target is to find angle.

I have used formula: $\tan\theta= \frac{m2-m1}{1 + |m2||m1|}$

First I convert equations:

$y = -3x - 2$ and

$-2y = -4x + 5$ =>

$-y = 2x + \frac{5}{2}$ =>

$y = -2x - \frac{5}{2}$

Now I got: $\tan\theta= \frac{-2-3}{1+-2.(3)}$, which will result of $\frac{-5}{-5}$, which in angles is 57.29°, but the right answer is: $\frac{\pi}{4}$. Where is my mistake. Please explain. Thank you.

Answer 1

Its easy..You have almost solved it . You have already shown $\tan(\theta)= -5/-5= 1$ All that remains is to find a special value of theta to satisfy the equation.. taking $\arctan$ on both sides...One finds the answer to be $\pi/4$... $$\sin(\pi/4)=\cos(\pi/4)$$ $$\tan(\pi/4)=1.$$

Answer 2

You made an arithmetic mistake. Second equation should rearrange to y=2x+5/2.