Posts Tagged ‘polar coordinates’

Problem 712

A fire truck is en route to an address that is six blocks east and seven blocks south of the fire station. Using the fire station as the pole and the east direction as the polar axis, express the fire truck’s destination in polar coordinates. Round the coordinates to the nearest unit. Express θ in degrees.

 

Solution:-

 

(9, -49°)

Problem 710

 

The letters x and y represent rectangular coordinates. Write the following equation using polar coordinates (rθ).

y = x

 

Solution:-

 

x = r * cosθ

y = r * sinθ

give the equation y = x

r cosθ = r sinθ (divide both sides by r cosθ)

1 = tanθ

tanθ = 1

 

Problem 702

Convert the rectangular coordinates (4,4i\sqrt{3})into polar coordinates.

 

Solution:-

 

r^{2} = x^{2} + y^{2}

r^{2 }= 4^{2} + (4sqrt(3))^{2}

{r^2} = 16+48

r^{2} = 64

r = 8

Now  we are find θ =tan^{-1}\frac{y}{x}

= tan^{-1}\frac{4\sqrt{3}}{4}

θ = 60°

So the poler coordinate (8, 60°)