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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.

2 Answers 2

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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 $\pi/4$... $$\sin(\pi/4)=\cos(\pi/4)$$ $$\tan(\pi/4)=1.$$

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    Imagine that I do not know the answer. How can I get it? – 2017-02-13
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    Which is the formula that I get from $\frac{-5}{-5}$ to $\frac{\pi}{4}$? – 2017-02-13
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    Its generally hard to find value of $\theta$ for many angles without a calculator..but you can easily find values of $\theta$ for some basic angles( like multiples of 15). – 2017-02-13
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    You are not answering my question at all – 2017-02-13
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    Think it this way....Which value of $\theta$ when evaluated with a tangent function gives 1 ?....I can only think of one which remains in the arctan's domain.....that is between -90 to 90 – 2017-02-13
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    Please don't answer me with questions. Either explain either delete your comment – 2017-02-13
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    Could you please clarify what are you not getting? – 2017-02-13
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    Read my second comment – 2017-02-13
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    There is no formula for it...You just have to find the value satisfying the equation (either using a calculator or by your own if you remember tan($\theta$) of special angles) ...DO you get it now? – 2017-02-13
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    From calculator $\tan\theta$ is 57.29°, and $\frac{\pi}{4}$ is 45° – 2017-02-13
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    Have you studied about inverse functions of trigonometric functions? – 2017-02-13
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    No, I have ask a straight question. I am not professor and stop post comments that did not target to answer my question – 2017-02-13
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    Think like this tan($\theta$)=1=tan($\pi$/4) .. SO $\theta$ equals $\pi$/4 – 2017-02-13
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    Why not tan(θ)=1=tan(π/14)? Why $\theta$ should be equals to $\pi/4$? – 2017-02-13
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    Why $\pi/4$ why not $\pi/10$ or any number? Why 4? – 2017-02-13
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    Because tan($\pi^2$/4) is -0.799.. which is not equal to 1 – 2017-02-13
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    because only tan($\pi$/4)=1...No other value of $\theta$ gives 1 – 2017-02-13
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    57.29° is more close to 60°, not to 45°. – 2017-02-13
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    so why not $\frac{\pi}{3}$ – 2017-02-13
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    Search on google for an arctangent calculator and type 1 .. you will get your answer – 2017-02-13
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    http://www.rapidtables.com/convert/number/radians-to-degrees.htm – 2017-02-13
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    Evaluate tan ($\pi$/3)...It is not equal to 1 – 2017-02-13
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    I will not except this answer until someone explain to me what is the connection or how to convert $\frac{-5}{-5}$ to $\frac{\pi}{4}$ – 2017-02-13
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    http://www.rapidtables.com/calc/math/Arctan_Calculator.htm .. type 1... As you want tan($\theta$)=1 – 2017-02-13
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    Did you get it? – 2017-02-13
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    You’re going to have much better results on this site if you stop being so combative and demanding things from people who are trying to help you. – 2017-02-13
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You made an arithmetic mistake. Second equation should rearrange to y=2x+5/2.