Please Help. Convert the following direction into desired one requested in each case.

Question

1.  a) Polar coordinate (3km/h (fraction form), 60^o), convert into both true and quadrant bearing.

b) Scalar component (-5, -10), convert into polar coordinate and true bearing.

Answer 1

The sides of the triangle is obtained from a special triangle (30-60-90) or from Pythagorean Theorem.

or

x = 3 cos 60˚ = 1.5

y = 3 sin 60˚ = 3√3 / 2 ~ 2.6



a) answer: (1.5 km/h, 3√3 / 2 km/h)

b) located in the third quadrant

r² =(-5)²+(-10)²

r =√35

tan θ = -10/(-5) = 2

θ = tan^-1 (2)

θ = 63.43˚ (This is located on the first quadrant. We need to add 180˚)

θ = 243.43˚

Therefore, the Polar for rectangular (-5,-10) is (√35, 243.43˚)