How do you convert theta= 1.34θ=1.34 into cartesian form?

1 Answer
May 8, 2018

y = x tan(1.34) quad for x > 0

Explanation:

1.34 radians is around 77^circ, comfortably in the first quadrant.

theta = 1.34 is thus a ray from the origin into the first quadrant. It's not the line through the angle, because the part of the line in the third quadrant satisfies theta = 1.34 + pi.

So, understanding x>0, y>0 we take tangents and get

tan theta = tan(1.34)

Since

x = r cos theta

y = r sin theta

we get

tan theta = y/x

and our equation becomes

y/x = tan(1.34)

y = x tan(1.34) quad for x > 0.

That's the ray through the origin and the first quadrant with slope tan(1.34). We explicitly exclude x=0 which doesn't have the required angle.