Question

Find the values of theta and p, if the equation xcostheta + ysintheta = p is the normal form of the line root 3x + y + 2 = 0

Answer 1

Thank you for asking this question. Here is your answer:

When we form the equation it would be like this:

3–√x+y+2=0

There is another way to write this equation: −3–√x−y=2

When we divide both sides by 2 we will get this

−3–√2x−12y=1

cosθ=−3–√2 and sinθ=12, and p=1

We know that both cosθ and sinθ are negatives, so we will get this:

θ=π+π6=7π6

So the values of θ and p are 7π6 and 1

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