Answer to Question #103562 in Calculus for talal Al-Zuraiqi

Question

Convert the following vectors;
75 m/s on a bearing of 295° to Cartesian form
[-3, -8] to direction/magnitude form

Answer 1

x = r × cos( θ ) = 75 *  cos(295°) = 31.7 m/s

y = r × sin( θ ) = 75 * sin(295°) = -68.0 m/s

Answer: [31.7, -68.0]

r = √ ( x² + y² ) = √ ( (-3)² + (-8)² ) = 8.54

θ = tan^-1 ( y / x ) = tan^-1 ( -8 / -3 ) = 69.4°

Answer: θ = 69.4°, r = 8.54