Question

If the polar coordinates of a point are given by (9.77 m, θ) and the rectangular coordinates are given by (x, 3.50 m), determine values for θ and x.

Answer 1

Answer:

the solutions are (9,12 m , 0.366 rad) and (-9,12 m ,  1.936 rad)

Step-by-step explanation:

given the polar coordinates (r=9.77 m ,  θ) and  (x, y=3.50 m) , since we know that

x²+y²=r² → x = ±√(r²-y²) = ±√(9.77 ²-3.50 ²)= ± 9,12 m

then

x = r* cos θ → for θ = cos ⁻¹ (x/r)

thus

for x= 9,12 m → θ = cos ⁻¹ (9,12 m/9.77 m) = 0.366 rad

for x= -9,12 m → θ =  0.366 rad + π/2 rad = 1.936 rad

therefore the solutions are (9,12 m , 0.366 rad) and (-9,12 m ,  1.936 rad)