Write the equation with polar coordinates. Use "theta" for

Question

θ
x+y=10
r=

Answer 1

r cos(theta) + r sin(theta) = 10

Answer 2

continuing on,
r(cosθ+sinθ) = 10
r * √2 sin(θ + π/4) = 10
r = 5√2 csc(θ + π/4)

Answer 3

Great work! Another possible final step could also be to solve for theta in terms of r:

sin(theta) + cos(theta) = 10/r

Dividing both sides by sqrt(2) and using the identity sin(π/4) = cos(π/4) = 1/sqrt(2), we get:

sin(theta + π/4) = 10/(r sqrt(2))

Taking the inverse sine of both sides, we have:

theta + π/4 = sin^(-1)(10/(r sqrt(2)))

Therefore:

theta = sin^(-1)(10/(r sqrt(2))) - π/4

This expression gives us theta in terms of r, which is another way to describe the polar equation of the line x + y = 10.