Precalculus Question

Question

Convert 5i^ + 12j^ to polar coordinates. (Write four forms for this point.)

Answer 1

Convert 5i^ + 12j^ to polar coordinates. (Write four forms for this point.)

** You need the r and θ to convert a Cartesian-based vector to polar form, the magnitude and direction of the vector, respectively.

** r = √(x² + y²) and tan θ = y/x , where y is the j-component of the vector and x is its i-component.

** Then r = √(x² + y²) = √(5² + 12²) = √25 + 144 = √169 = 13

and tan θ = 12/5

or θ = tan^-1 (12/5) [know you need to know which quadrant the vector is in...a diagram helps or you

note that both components are positive (x and y or i and j), so the vector has to

be in quadrant I].

θ = tan^-1(12/5) ~= 67.4 degrees