Question

Find the acute angle between the lines 2y + x =1 , x + 3y = 6 what is tan theta


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Answer 1

Answer:

2x−y=4 , so

y = 2x - 4 and the slope of this line is 2

so the angle of this line with the positive x-axis is  tan−1(2)  

3x+y=3 , so

y = 3 - 3x, and the slope of this line is -3

so the angle of this line with the positive x-axis is  tan−1(−3)  

since  tan−1(−3)  is in the second quadrant and  tan−1(2)  is in the first quadrant

the acute angle between the two lines is therefore  tan−1(−3)−tan−1(2)=45°  

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You can verify this final result by using the following compound angle identity for tangent . . .

tan(A−B)≡tanA−tanB1+tanAtanB  

thus we can let  C=tan−1(−3)−tan−1(2)  

then  tanC=tan[tan−1(−3)−tan−1(2)]  

tanC=tan[tan−1(−3)]−tan[tan−1(2)]1+tan[tan−1(−3)]tan[tan−1(2)]  

tanC=−3−21+(−3)(2)=−51–6=−5−5=1  

tanC=1  

so C must be 45°

5.5K viewsView 2 Upvoters · Answer requested by Lee On Tyn

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