How do you convert #theta= 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.