Express the Cartesian coordinates ( - 5,5) in polar coordinates in at least two different ways. Write the point in polar coordinates with an angle in the range 0 < = theta < 2pi (Type an ordered pair. Type an exact answer, using pi as needed.) Write the point in polar coordinates with an angle in the range - 2pi < = theta < 0. [ ] (Type an ordered pair. Type an exact answer. using pi as needed.)

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lucianoangelini92 lucianoangelini92 · Answer 1 · 2020-01-25T13:12:24+01:00

Answer:

one way) (r,θ) = (5,3/4π)

other way) (r,θ) = (5, 7/4*π)

Step-by-step explanation:

first way

x= r*cos θ

y= r*sin θ

then

tg θ = y/x → θ = tan ⁻¹ (y/x) = tan ⁻¹ (5/-5) = - tan ⁻¹ 1 = π- π/4 = 3/4π

then if

r=√(x²+y²)= r=√((-5)²+5²) = 5

therefore

(r,θ) = (5,3/4π)

another way would be

x= r*sin θ

y= r*cos θ

then

tg θ = x/y → θ = tan ⁻¹ (x/y) = tan ⁻¹ (-5/5) = - tan ⁻¹ 1 = -π/4 or 2*π- π/4 = 7/4*π

then since r=5 , the polar coordinates would be

(r,θ) = (5, 7/4*π)