calculus question

Question

(1, - 1) convert to polar coordinates. Show steps

Answer 1

x = r cos T

y = r sin T

x^2 + y^2 = r^2

x=1; y=-1

So r^2 = (1)^2 + (-1)^2

= 1 + 1

= 2

r = sqrt(2)

x = r cos T

1 = sqrt(2) * cos T

1/sqrt(2) = cos T

sqrt(2)/2 = cos T <--- rationalizes the denominator

T = 45 or 315 as cosine is positive in quadrant 1 and 4

check:

y = r sin T

-1 = sqrt(2) * sin T

-sqrt(2)/2 = sin T

T = 225 or 315 as sine is negative in quadrant 3 and 4

conclusion:

r = sqrt(2)

angle T = 315 = 7*pi/4

Answer 2

Polar coordinates are in the form (r, θ). To find these, lets plot the point (1, -1):

r = √[1² + (-1)²] = √2

θ = 2π - π/4 = 7π/4

So the point, in polar coordinates, is (√2, 7π/4)